Solve 5 ^ (6x) = (625) ^ 3 | 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

$$5^{6x}=(625)^{3}$$

Solve for x

$x=2$

Steps Using Definition of Logarithm

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

$$5^{6x}=244140625$$

Take the logarithm of both sides of the equation.

$$\log(5^{6x})=\log(244140625)$$

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

$$6x\log(5)=\log(244140625)$$

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

$$6x=\frac{\log(244140625)}{\log(5)}$$

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

$$6x=\log_{5}\left(244140625\right)$$

Divide both sides by $6$.

$$x=\frac{12}{6}$$

Solve for x (complex solution)

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