Question

find x of 2 log 5+ 1/2 log 16-log4.= log x.​

Answer 1

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Answer 2

Question ;

find x if

2 log 5+ 1/2 log 16-log4= log x.

properties of logarithm

1) log a + log b = log ( ab)

2) log a - log b = log (a/b)

$3) \: \: \: n log(x) = log(x {}^{n} )$

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$2 log(5) + \frac{1}{2} log(16) - log(4) = log(x)$

now use property 3

$n log(x) = log(x)$

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$log(5 {}^{2} ) + log(16 {}^{ \frac{1}{2} } ) - log(4) = log(x)$

$log(25) + log(4) - log(4) = log(x)$

$log(25) = log(x)$

now equate both LHS and RHS

therefore , x = 25

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