Question

1. (log5 3) (log2 625) equals​

Answer 1

Answer:

The value of \log_2 (\log_5 625)=2log2(log5625)=2 .

Step-by-step explanation:

We have,

\log_2 (\log_5 625)log2(log5625)

To find, the value of \log_2 (\log_5 625)=?log2(log5625)=?

∴ \log_2 (\log_5 625)log2(log5625)

=\log_2 (\log_5 5^{4} )=log2(log554)

=\log_2 (4\log_5 5)=log2(4log55)

[ ∵ \log a^{m}=m\log alogam=mloga

=\log_2 (4\times 1)=log2(4×1)

[ ∵\log_a a=1logaa=1

=\log_2 2^{2}=log222

=2\log_2 2=2log22

=2\times 1=2=2×1=2

Hence, the value of \log_2 (\log_5 625)=2log2(log5625)=2 .