Solve 5^3x-7=1/25

$$5 ^ { 3 x - 7 } = \frac { 1 } { 25 }$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps Using Definition of Logarithm

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

$$5^{3x-7}=\frac{1}{25}$$

Take the logarithm of both sides of the equation.

$$\log(5^{3x-7})=\log(\frac{1}{25})$$

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

$$\left(3x-7\right)\log(5)=\log(\frac{1}{25})$$

Divide both sides by \log(5).

$$3x-7=\frac{\log(\frac{1}{25})}{\log(5)}$$

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

$$3x-7=\log_{5}\left(\frac{1}{25}\right)$$

Add 7 to both sides of the equation.

$$3x=-2-\left(-7\right)$$

Divide both sides by 3.

$$x=\frac{5}{3}$$

Solve for x (complex solution)

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

$$n_{1}\in \mathrm{Z}$$