Solve -3.3*15^n=-76

$$- 3.3 \cdot 15 ^ { n } = - 76$$

Solve for n

$$n=\log_{15}\left(\frac{760}{33}\right)\approx 1.158328184$$

Steps Using Definition of Logarithm

Divide both sides by -3.3.

$$15^{n}=\frac{-76}{-3.3}$$

Expand \frac{-76}{-3.3} by multiplying both numerator and the denominator by 10.

$$15^{n}=\frac{-760}{-33}$$

Fraction \frac{-760}{-33} can be simplified to \frac{760}{33} by removing the negative sign from both the numerator and the denominator.

$$15^{n}=\frac{760}{33}$$

Take the logarithm of both sides of the equation.

$$\log(15^{n})=\log(\frac{760}{33})$$

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

$$n\log(15)=\log(\frac{760}{33})$$

Divide both sides by \log(15).

$$n=\frac{\log(\frac{760}{33})}{\log(15)}$$

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

$$n=\log_{15}\left(\frac{760}{33}\right)$$

Solve for n (complex solution)

$$n=\frac{i\times 2\pi n_{1}}{\ln(15)}+\log_{15}\left(\frac{760}{33}\right)$$

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