Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{Findthevalueofxsuchthat\times {2}^{5x}}{{2}^{x}}={\sqrt[2}^{20]{5}}\]
Regroup terms.
\[\frac{ndttthhhvaaluuofxscFiee\times {2}^{5x}}{{2}^{x}}={\sqrt[2}^{20]{5}}\]
Simplify \(ndttthhhvaaluuofxscFiee\times {2}^{5x}\) to \(nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxscFiee\times {2}^{5x}\).
\[\frac{nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxscFiee\times {2}^{5x}}{{2}^{x}}={\sqrt[2}^{20]{5}}\]
Use Product Rule : \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxscFi{e}^{2}\times {2}^{5x}}{{2}^{x}}={\sqrt[2}^{20]{5}}\]
Regroup terms.
\[\frac{Fi{e}^{2}nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{5x}}{{2}^{x}}={\sqrt[2}^{20]{5}}\]
Simplify \(\frac{Fi{e}^{2}nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{5x}}{{2}^{x}}\) to \(Fi{e}^{2}nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}\).
\[Fi{e}^{2}nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}={\sqrt[2}^{20]{5}}\]
Divide both sides by \(Fi\).
\[{e}^{2}nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi}\]
Divide both sides by \({e}^{2}\).
\[nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi}}{{e}^{2}}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi}}{{e}^{2}}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}}\).
\[nd{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}}\]
Divide both sides by \(d\).
\[n{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}}}{d}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}}}{d}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d}\).
\[n{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d}\]
Divide both sides by \({t}^{3}\).
\[n{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d}}{{t}^{3}}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d}}{{t}^{3}}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}}\).
\[n{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}}\]
Divide both sides by \({h}^{3}\).
\[nv{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}}}{{h}^{3}}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}}}{{h}^{3}}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}}\).
\[nv{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}}\]
Divide both sides by \(v\).
\[n{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}}}{v}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}}}{v}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v}\).
\[n{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v}\]
Divide both sides by \({a}^{2}\).
\[nl{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v}}{{a}^{2}}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v}}{{a}^{2}}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}}\).
\[nl{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}}\]
Divide both sides by \(l\).
\[n{u}^{2}ofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}}}{l}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}}}{l}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l}\).
\[n{u}^{2}ofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l}\]
Divide both sides by \({u}^{2}\).
\[nofxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l}}{{u}^{2}}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l}}{{u}^{2}}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}}\).
\[nofxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}}\]
Divide both sides by \(o\).
\[nfxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}}}{o}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}}}{o}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}o}\).
\[nfxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}o}\]
Divide both sides by \(f\).
\[nxsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}o}}{f}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}o}}{f}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}of}\).
\[nxsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}of}\]
Divide both sides by \(x\).
\[nsc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}of}}{x}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}of}}{x}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofx}\).
\[nsc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofx}\]
Divide both sides by \(s\).
\[nc\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofx}}{s}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofx}}{s}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxs}\).
\[nc\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxs}\]
Divide both sides by \(c\).
\[n\times {2}^{4x}=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxs}}{c}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxs}}{c}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc}\).
\[n\times {2}^{4x}=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc}\]
Divide both sides by \({2}^{4x}\).
\[n=\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc}}{{2}^{4x}}\]
Simplify \(\frac{\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc}}{{2}^{4x}}\) to \(\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}}\).
\[n=\frac{{\sqrt[2}^{20]{5}}}{Fi{e}^{2}d{t}^{3}{h}^{3}v{a}^{2}l{u}^{2}ofxsc\times {2}^{4x}}\]
n=5^(1/2^20)/(Fi*e^2*d*t^3*h^3*v*a^2*l*u^2*o*f*x*s*c*2^(4*x))
