Solve 5 If 4 ^ 3 = 4 ^ x then find 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

$$4 ^ { 3 } = 4 ^ { x } , x$$

Solve for x

$x=3$

Steps Using Definition of Logarithm

Calculate $4$ to the power of $3$ and get $64$.

$$64=4^{x}$$

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

$$4^{x}=64$$

Take the logarithm of both sides of the equation.

$$\log(4^{x})=\log(64)$$

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

$$x\log(4)=\log(64)$$

Divide both sides by $\log(4)$.

$$x=\frac{\log(64)}{\log(4)}$$

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

$$x=\log_{4}\left(64\right)$$

Solve for x (complex solution)

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