Solve 8225(10295)^n=3750

$$8225 ( 10295 ) ^ { n } = 3750$$

Solve for n

$$n=\log_{10295}\left(\frac{150}{329}\right)\approx -0.085007825$$

Steps Using Definition of Logarithm

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

$$8225\times 10295^{n}=3750$$

Divide both sides by 8225.

$$10295^{n}=\frac{150}{329}$$

Take the logarithm of both sides of the equation.

$$\log(10295^{n})=\log(\frac{150}{329})$$

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

$$n\log(10295)=\log(\frac{150}{329})$$

Divide both sides by \log(10295).

$$n=\frac{\log(\frac{150}{329})}{\log(10295)}$$

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

$$n=\log_{10295}\left(\frac{150}{329}\right)$$