Solve 2 ^ (2x) * 2 ^ 4 = 2 ^ 6 | 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

$$2^{2x}\times2^{4}=2^{6}$$

Solve for x

$x=1$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$16\times 2^{2x}=64$$

Divide both sides by $16$.

$$2^{2x}=4$$

Take the logarithm of both sides of the equation.

$$\log(2^{2x})=\log(4)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$2x\log(2)=\log(4)$$

Divide both sides by $\log(2)$.

$$2x=\frac{\log(4)}{\log(2)}$$

By the change-of-base formula $\frac{\log(a)}{\log(b)}=\log_{b}\left(a\right)$.

$$2x=\log_{2}\left(4\right)$$

Divide both sides by $2$.

$$x=\frac{2}{2}$$

Solve for x (complex solution)

$x=\frac{\pi n_{1}i}{\ln(2)}+1$
$n_{1}\in \mathrm{Z}$