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

Answer:

x = 2

Step-by-step explanation:

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

Taking logarithm to base 10 on both sides we get

$log5^x=log25$

From logarithm property

$logy^x=xlogy$

$\Rightarrow xlog5=log25\\\Rightarrow x=\frac{log25}{log5}\\\Rightarrow x=2$

$\therefore x=2$

Also we know that

$5\times 5=25\\\Rightarrow 5^2=25$

Hence, x = 2