If log3(81) = x, what is the value of x?

If log3(81) = x, what is the value of x?

Correct Answer: 4

Step 1: Understand the question. We have log3(81) = x, which means we want to find out what power we need to raise 3 to in order to get 81.
Step 2: Rewrite the equation in exponential form. This means we can say that 3 raised to the power of x equals 81: 3^x = 81.
Step 3: Find out what 81 is in terms of powers of 3. We know that 81 can be written as 3 multiplied by itself four times: 81 = 3 * 3 * 3 * 3 = 3^4.
Step 4: Now we can set the two expressions equal to each other: 3^x = 3^4.
Step 5: Since the bases (3) are the same, we can set the exponents equal to each other: x = 4.
Step 6: Therefore, the value of x is 4.

Logarithms – Understanding the relationship between exponents and logarithms, specifically how to express a number as a power of a base.
Exponential Equations – Recognizing that logarithmic equations can be solved by rewriting them in exponential form.