Question

help me with this

log[5]√125

Answer 1

\[\large \log_5 \sqrt{125} = \log_5 5^{3/2} = \frac{3}{2} \log_5 5 = \cdots\]

Answer 2

@ParthKohli sorry i don't get it

Answer 3

@bless just remember that
\[\log_{a}a = 1 \]
in your case
\[\frac{ 3 }{ 2 }\log_{5}5 = x \]
Hence, x = ?

Answer 4

Sorry, I am back. Can we write \(\sqrt{125} = \sqrt{5^3} = 5^{3/2}\)?

Answer 5

@ParthKohli yes

Answer 6

That is what I have done here. Also note that \(\log\left(a^m\right) = m \log(a)\)

Answer 7

why did √5^3 turns into 5^3/2?

Answer 8

@ParthKohli ?