Solve (5)^(x)\times(5)^(-3)=(5)^(5) | 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

$${ 5 }^{ x } \times { 5 }^{ -3 } = { 5 }^{ 5 }$$

Solve for x

$x=8$

Steps Using Definition of Logarithm

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

$$\frac{1}{125}\times 5^{x}=3125$$

Multiply both sides by $125$.

$$5^{x}=390625$$

Take the logarithm of both sides of the equation.

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

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

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

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

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

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

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

Solve for x (complex solution)

$x=\frac{2\pi n_{1}i}{\ln(5)}+8$
$n_{1}\in \mathrm{Z}$