Question

Evaluate the following by converting into exponential form:

log₉ 243

Answer 1

Given: log₉ 243

Step-wise calculation:

1. Let log₉ 243 = x,

So 9^x = 243.

2. Write both sides with base 3:

9 = 3² and 243 = 3⁵,

So (3²)^x = 3⁵.

3. Simplify:

3^2x = 3⁵ 

⇒ 2x = 5

⇒ `x = 5/2`

`log_9 243 = 5/2`

log₉ 243 = 2.5