If log3(27) = x, what is the value of x?

If log3(27) = x, what is the value of x?

Correct Answer: 3

Step 1: Understand the question. We have log3(27) = x. This means we want to find out what power we need to raise 3 to in order to get 27.
Step 2: Rewrite 27 as a power of 3. We know that 27 can be written as 3 raised to the power of 3, which is 3^3.
Step 3: Set up the equation. Since log3(27) = x, we can replace 27 with 3^3. So now we have log3(3^3) = x.
Step 4: Use the property of logarithms. The logarithm logb(b^y) = y. In our case, log3(3^3) = 3.
Step 5: Conclude the value of x. Therefore, x = 3.

Logarithms – Understanding the relationship between exponents and logarithms, specifically how to convert between the two forms.
Exponential Equations – Recognizing that 27 can be expressed as a power of 3, which is essential for solving logarithmic equations.