Solve (5 ^ (4x)) / (5 ^ - 7) = 5 ^ 15 | 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

$$5^{4x}\div5^{-7}=5^{15}$$

Solve for x

$x=2$

Steps Using Definition of Logarithm

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

$$78125\times 5^{4x}=30517578125$$

Divide both sides by $78125$.

$$5^{4x}=390625$$

Take the logarithm of both sides of the equation.

$$\log(5^{4x})=\log(390625)$$

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

$$4x\log(5)=\log(390625)$$

Divide both sides by $\log(5)$.

$$4x=\frac{\log(390625)}{\log(5)}$$

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

$$4x=\log_{5}\left(390625\right)$$

Divide both sides by $4$.

$$x=\frac{8}{4}$$

Solve for x (complex solution)

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