Question

Simplify the following:

`logsqrt(125)/log25`

Answer 1

`logsqrt(125)/log25`

Step 1: Simplify the numerator:

`logsqrt(125)`

= `log (125)^(1/2)`

= `1/2 log 125`

Step 2: Substitute into the expression:

`(1/2 log 125)/log 25`

= `1/2 * (log 125)/(log 25)`

Step 3: Use change of base rule:

`(log 125)/(log 25)`

= log₂₅ 125

Now, 25 = 5² and 125 = 5³

So, log₂₅ 125

= `log_(5^2) 5^3`

= `3/2`

Step 4: Substitute back:

`1/2 xx 3/2`

= `3/4`