Given logx25-logx5=2-logx1125; find x - Maths - Indices and Logarithms

Question

Given log x 25 - log x 5 = 2 - log x 1 125 ; find x

Abhishek Kr. Jha · Accepted Answer

Dear student,
Here is the solution of your asked query:
logx25-logx5=2-logx1125⇒logx25-logx5+logx1125=2⇒logx255+logx1125=2       {using loga-logb=logab}⇒logx5+logx1125=2⇒logx5×1125=2                {using loga+logb=loga×b}⇒logx125=2⇒x2=125⇒x2=152⇒x=15
Regards

Given log x 25 - log x 5 = 2 - log x 1 125 ; find x.

Given $\log_{x} 25 - \log_{x} 5 = 2 - \log_{x} \frac{1}{125}$ ; find x.