Solve (t) / ((5 ^ x - 5 ^ (x - 1))/(4 * 5 ^ (x - 1))) = 1 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(t):\frac{5^{x}-5^{x-1}}{4\times5^{x-1}}=1$$

Solve for t

$t=1$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{4}{5^{1-x}\left(-\frac{1}{5^{1-x}}+5^{x}\right)}t=1$$

Divide both sides by $4\left(5^{x}-5^{-\left(-x+1\right)}\right)^{-1}\times 5^{-\left(-x+1\right)}$.

$$\frac{\frac{4}{5^{1-x}\left(-\frac{1}{5^{1-x}}+5^{x}\right)}t\times 5^{1-x}\left(-\frac{1}{5^{1-x}}+5^{x}\right)}{4}=\frac{5^{1-x}\left(-\frac{1}{5^{1-x}}+5^{x}\right)}{4}$$

Dividing by $4\left(5^{x}-5^{-\left(-x+1\right)}\right)^{-1}\times 5^{-\left(-x+1\right)}$ undoes the multiplication by $4\left(5^{x}-5^{-\left(-x+1\right)}\right)^{-1}\times 5^{-\left(-x+1\right)}$.

$$t=\frac{5^{1-x}\left(-\frac{1}{5^{1-x}}+5^{x}\right)}{4}$$

Divide $1$ by $4\left(5^{x}-5^{-\left(-x+1\right)}\right)^{-1}\times 5^{-\left(-x+1\right)}$.

$$t=1$$

Solve for x (complex solution)

$x\in \mathrm{C}$
$t=1$

Solve for x

$x\in \mathrm{R}$
$t=1$