Solve -3*5^v-7=-70

$$- 3 \cdot 5 ^ { v - 7 } = - 70$$

Solve for v

$$v=\log_{5}\left(\frac{14}{3}\right)+8\approx 8.957132319$$

Steps Using Definition of Logarithm

Divide both sides by -3.

$$5^{v-7}=\frac{-70}{-3}$$

Fraction \frac{-70}{-3} can be simplified to \frac{70}{3} by removing the negative sign from both the numerator and the denominator.

$$5^{v-7}=\frac{70}{3}$$

Take the logarithm of both sides of the equation.

$$\log(5^{v-7})=\log(\frac{70}{3})$$

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

$$\left(v-7\right)\log(5)=\log(\frac{70}{3})$$

Divide both sides by \log(5).

$$v-7=\frac{\log(\frac{70}{3})}{\log(5)}$$

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

$$v-7=\log_{5}\left(\frac{70}{3}\right)$$

Add 7 to both sides of the equation.

$$v=\frac{\ln(\frac{70}{3})}{\ln(5)}-\left(-7\right)$$