Question Type 4: Using logarithms to solve simple exponential equations Exercises

Solve for $x$ in the equation $7^{2x} = 49^{x+1}$.

Solve for $x$ in the equation $2^{3x - 1} = 5^{x+2}$. Give your answer in exact form.

Solve for $x$ in the equation $2^{x+2} = 5^{1-x}$.

Solve for $x$ in the equation $3^{x-4} = 7$.

Solve for $x$ in the equation $10^x = 3.56$.

Solve for $x$ in the equation $e^{2x} = 10$.

Solve for $x$ in the equation $5^{2x+1} = 125$.

Solve for $x$ in the equation $3^{2x+1} = \frac{1}{9}$.

Solve for $x$ in the equation $2^x = 23$.

Solve for $x$ in the equation $\left(\frac{1}{2}\right)^{x} = 16$.

Solve for $x$ in the equation $4^{x+1} = 8^{2x-1}$.

Solve for $x$ in the equation $9^x = 27^{x-2}$.