Question

Evaluate log3 81

Answer 1

Step-by-Step Solution

Step 1: Set up the equation

Let's set the expression equal to a variable, like x.

log₃ 81 = x

Our goal is to find the value of x.

Step 2: Convert the logarithm to its exponential form

The fundamental relationship between logarithms and exponents is:

logₐ b = c is the same as aᶜ = b

Using this rule, we can rewrite our equation log₃ 81 = x:

3ˣ = 81

Now, the problem is much simpler: we just need to find the power x that makes this equation true.

Step 3: Solve for x

We need to figure out how many times we multiply 3 by itself to get 81. Let's try it out:

• 3¹ = 3
• 3² = 3 × 3 = 9
• 3³ = 3 × 3 × 3 = 27
• 3⁴ = 3 × 3 × 3 × 3 = 81

We found it! 3 raised to the power of 4 is 81.

Step 4: State the final answer

Since we found that 3⁴ = 81, we can substitute 4 back in for x.

x = 4

Therefore:

log₃ 81 = 4