Question

# Solve the equation. Round your answers to the nearest hundredth. 8^x=12

Exponential growth and decay

Solve the equation. Round your answers to the nearest hundredth. $$8^x=12$$

$$\displaystyle{8}^{{x}}={12}$$ Given equation.
$$\displaystyle{{\log{{8}}}^{{x}}=}{\log{{12}}}$$ Take the log for both sides
$$\displaystyle{x}\cdot{\log{{8}}}={\log{{12}}}$$ Power rule of logarithms
$$\displaystyle{x}={\left(\frac{{\log{{12}}}}{{\log{{8}}}}\right)}$$ Divide both sided by log 8
$$x \sim 1.19$$ Using calculator.