Solve 16^10b=88

$$16 ^ { 10 b } = 88$$

Solve for b

$$b=\frac{\log_{2}\left(88\right)}{40}\approx 0.16148579$$

Steps Using Definition of Logarithm

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

$$16^{10b}=88$$

Take the logarithm of both sides of the equation.

$$\log(16^{10b})=\log(88)$$

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

$$10b\log(16)=\log(88)$$

Divide both sides by \log(16).

$$10b=\frac{\log(88)}{\log(16)}$$

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

$$10b=\log_{16}\left(88\right)$$

Divide both sides by 10.

$$b=\frac{\log_{2}\left(88\right)}{4\times 10}$$