Question

Simplify the following:

`log 64/log 32`

Answer 1

We are given:

`log 64/log 32`

Step 1: Express 64 and 32 as powers of 2

• 64 = 2⁶
• 32 = 2⁵

Step 2: Apply the logarithmic property

We can use the logarithmic property log a^b = b log a:

log 64 = log(2⁶) = 6 log 2

log 32 = log(2⁵) = 5 log 2

Step 3: Simplify the expression

Now the expression becomes:

`(6 log 2)/(5 log 2)`

Cancel log 2 from the numerator and denominator:

`6/5`