Question

simplify,log(logx to the power4)-log(logx)​

Answer 1

$\red { \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$


$\bold{log \: (log \: x {}^{4} ) \: - \: log \: (log \: x)} \\ \\ \\ \bold{ = log \: ( \frac{ \: \: log \: x {}^{4} \: \: }{log \: x}) } \\ \\ \\ \bold{ = log \: ( \frac{4 \: \cancel{log \: x}}{ \cancel{log \: x}} )} \\ \\ \\ \bold{ = log \: 4} \\ \\ \\ \bold{ = log \: (2) {}^{2} } \\ \\ \\ \bold{ = 2 \: log \: 2}$


$\underline{ \underline{ \bold{ \huge{ \red{ \: \: IDENTITIES \: \: USE \: \: }}}}}$

$\bold{1. \: \: log \:( \frac{m}{n}) = log \: m \: - \: log \: n } \\ \\ \\ \bold{2. \: \: log \: a {}^{x} = x \: log \: a }$

Answer 2

$\underline{ \underline{ \red{ \: \: SOLUTION\: \: }}}$


$\underline{ \: To \: \: Simplify \: : }$


$log \: (log \: x {}^{4} ) - log \: (log \:x)$



$Here, \\ \\ \underline{ FORMULAS \: \: USEE \: :} \\ \\ 1. \: log \: ( \frac{a}{b} ) = log \: a \: - \: log \: b \\ \\ 2. \: log \: x {}^{a} = a \: log \: x$



$\underline{Now, \: \: come \: \: to \: \: the \: \: question \: \: }$



$log \: (log \: x {}^{4}) \: - \: log \: (log \: x) \\ \\ = log \: ( \: \frac{log \: x {}^{4} }{log \: x} \: ) \\ \\ = log \: ( \frac{4 \: \cancel{ log \: x}}{ \cancel{log \: x} }) \\ \\ = log \: 4 \\ \\ = log \: (2) {}^{2} \\ \\ = 2 \: log \: 2$



$\underline{ \underline{ \red{ \: \: ANSWER\: \: }}}$



$\boxed{ \: log \: ( \: log \: x {}^{4}) \: - \: log \: (log \: x) \: = 2 \: log \: 2 \: }$