Question

given 2log x+1 = log 250 find x

Answer 1

2logx+1=log250

consider LHS,

log250=log(25×10)
=log25+log10
=log25 +1
comparing with RHS ie,

2logx+1=log25+1
ie,
2logx=log25

$log {5}^{2} = log25$
X=5

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The value of x is 5.}}}$

Step-by-step explanation:  We will be using the following properties of logarithms :

$(i)~\log10=1,\\\\(ii)~b\log a=\log a^b,\\\\(iii)~loga-\log b=\log\dfrac{a}{b}.$

We have

$2\log x+1=\log250\\\\\Rightarrow \log x^2=\log250-1\\\\\Rightarrow \log x^2=\log250-\log10\\\\\Rightarrow \log x^2=\log\dfrac{250}{10}\\\\\Rightarrow x^2=25\\\\\Rightarrow x=\pm5.$

Since the logarithm of a negative value is not defined, so x = 5.

Thus, the required value of x is 5.