Question

${a}^{ \frac{logb(logb \: x)}{log \: a} }$
find the value it is important ​

Answer 1

QUESTION:

${a}^{ \frac{ \log(b)( \log_{b}(x) )}{ \log(a) } }$

ANSWER:

Using

log_b(a) = log(a)/log(b)

$= {a}^{ \frac{ \log(b) \times \frac{ \log(x) }{ \log(b) } }{ \log(a) } }$

log(b) get cancelled

$= {a}^{ \frac{ \log(x) }{ \log(a) } }$

We know that

log (a)/log (b) = log_b (a)

$= {a}^{ \log_{a}(x) }$

Using

${x}^{ \log_{x}(y) } = y$

$= x$

CONCEPTS USED:

⟩⟩ LOGARITHMS

Answer 2

Answer:

$a {}^{ log(b)( log_{b}(x) ) \div log(a) } = x$

Step-by-step explanation:

$a {}^{ log(b)( log_{b}(x) \div log(a) } \\ we \: know \: that \\ = > log_{a}(b) = log(b) \div log(a) \\ = > a {}^{ log(b) log(x ) \div log(b) \div log(a) } \\ = > a {}^{ log(x) \div log(a) } \\ = > a {}^{ log_{a}(x) } \\ we \: know \: that \\ = > x^{ log_{x}(y) } = y \\ = > a {}^{ log_{a}(x) } = x$