Solve 4*7^n=148

$$4 \times { 7 }^{ n } = 148$$

Solve for n

$$n=\log_{7}\left(37\right)\approx 1.85564473$$

Steps Using Definition of Logarithm

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

$$4\times 7^{n}=148$$

Divide both sides by 4.

$$7^{n}=37$$

Take the logarithm of both sides of the equation.

$$\log(7^{n})=\log(37)$$

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

$$n\log(7)=\log(37)$$

Divide both sides by \log(7).

$$n=\frac{\log(37)}{\log(7)}$$

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

$$n=\log_{7}\left(37\right)$$