If log_x(81) = 4, what is the value of x?

If log_x(81) = 4, what is the value of x?

Correct Answer: 3

Step 1: Understand the equation log_x(81) = 4. This means that x raised to the power of 4 equals 81.
Step 2: Rewrite the equation in exponential form: x^4 = 81.
Step 3: To find x, we need to take the fourth root of 81. This means we need to find a number that, when multiplied by itself four times, equals 81.
Step 4: Calculate the fourth root of 81. We know that 3 * 3 = 9 and 9 * 9 = 81, so 3 raised to the power of 4 equals 81.
Step 5: Therefore, x = 3.

Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
Exponential Form – Converting logarithmic expressions into exponential form to solve for the variable.