Question

Consider the logarithms base 5. For each logarithmic expression below, either calculate the value of the expression or explain why the expression does not make sense.

log5(25)

Answer 1

x = 2

Explanation:

`log_525=x\\\Rightarrow 5^x=25`

Taking logarithm to base 10 on both sides we get

`log5^x=log25`

From logarithm property

`logy^x=xlogy`

`\Rightarrow xlog5=log25\\\Rightarrow x=(log25)/(log5)\\\Rightarrow x=2`

`\therefore x=2`

Also we know that

`5* 5=25\\\Rightarrow 5^2=25`

Hence, x = 2