Question

1/(log 10 base x) +2 =2/log 10 base 0.5
solve and find the value of x​

Answer 1

$1 \div log_{x}(10) = log_{10}(x)$

(I'm representing log base 10 as log only!)

log x + 2 = 2log 0.5

=>0.5 = 1/2

$m log_{10}(x) = log_{10}(x {}^{m} )$

So 2log(1/2) = log((1/2)²) = log(1/4)

Now

log x + 2 = log (1/4)

$log_{10}(x) - log_{10}(y) = log_{10}(x \div y)$

So log x - log(1/4) = log ((x) /(1/4)) => log (4x)

So

log (4x) = -2

$log_{10}(x) = m \: \: = > \: 10 {}^{m} \: = \: x$

So 10^-2 = 4x

=> x = 1/400!