Question

solve the following can't find the value of of log base 2 log base 2 16 ​log base 2

Answer 1

THIS IS A SUM OF LOGARITHM
HERE GOES YOUR ANSWER----
$log_{2} log_{2} log_{2}16$

$log_{2} log_{2} log_{2} {2}^{4}$

$log_{2} log_{2}4 log_{2}2$ ☆[•.•log something with the same base is always 1]☆

$log_{2} log_{2}4$ [As already said..now we put the value]

$log_{2} log_{2} {2}^{2}$[●Check the power rule below]

$log_{2}2 log_{2}2$

$log_{2}2$

[1] Its the answer..

EXTRA INFORMATION:-

What is the power rule of logarithm?
When a logarithmic term has an exponent, then the logarithm power rule says that we can transfer the exponent to the front of the logarithm. Along with the product rule and the quotient rule, the logarithm power rule can be used for expanding and condensing logarithms. power rule of logarithms.
Applying this rule i this the sum.

Answer 2

${\huge {\mathfrak {Answer :-}}}$

✨${} log_2 \: log_2 \: log_2 \: 16$

${} = log_2 \: [ log_2 \: ( log_2 2^4 )]$

${} = log_2 \: [ log_2 \: ( 4 \times log_2 2)]$

${} = log_2 \: [ log_2 4]$

${} = log_2 \: [ log_2 2^2]$

${} = log_2 \: [ 2 \times log_2 2]$

${} = log_2 2$

${} = 1.$ ✔️

NOTE : ${} log_a a = 1$

$\bold {Thanks.. }$