Solve (2 ^ 12) / 8 = 2 ^ x | 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

$$2^{12}\div8=2^{x}.$$

Solve for x

$x=9$

Steps Using Definition of Logarithm

Multiply both sides of the equation by $8$.

$$2^{12}=8\times 2^{x}$$

Calculate $2$ to the power of $12$ and get $4096$.

$$4096=8\times 2^{x}$$

Swap sides so that all variable terms are on the left hand side.

$$8\times 2^{x}=4096$$

Divide both sides by $8$.

$$2^{x}=\frac{4096}{8}$$

Divide $4096$ by $8$ to get $512$.

$$2^{x}=512$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(512)$$

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

$$x\log(2)=\log(512)$$

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

$$x=\frac{\log(512)}{\log(2)}$$

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

$$x=\log_{2}\left(512\right)$$

Solve for x (complex solution)

$x=\frac{2\pi n_{1}i}{\ln(2)}+9$
$n_{1}\in \mathrm{Z}$