Question

If $7^{\log x}+x^{\log 7}=98$, then $\log _{10} \sqrt{x}=$

• A. 2
• B. 1
• C. $\frac{1}{2}$
• D. -1

Answer 1

Answer: (B)

(i) Use $\log a+\log b=\log a b$ and remove logarithms on both the sides and evaluate $(a-b)^2$.
(ii) Express RHS into single logarithm with coefficient 1.
(iii) Apply antilog and cancel the logarithms on both sides.
(iv) Divide LHS and RHS by $a b$ and obtain the required value.