Solve 2 ^ (3x - 7) = 256 | 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

$$2^{3x-7}=256$$

Solve for x

$x=5$

Steps Using Definition of Logarithm

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

$$2^{3x-7}=256$$

Take the logarithm of both sides of the equation.

$$\log(2^{3x-7})=\log(256)$$

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

$$\left(3x-7\right)\log(2)=\log(256)$$

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

$$3x-7=\frac{\log(256)}{\log(2)}$$

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

$$3x-7=\log_{2}\left(256\right)$$

Add $7$ to both sides of the equation.

$$3x=8-\left(-7\right)$$

Divide both sides by $3$.

$$x=\frac{15}{3}$$

Solve for x (complex solution)

$x=\frac{i\times 2\pi n_{1}}{3\ln(2)}+5$
$n_{1}\in \mathrm{Z}$