Question

If $\log x-5\log 3=-2$, then $x$ equals 

• A. $1.25$
• B. $0.81$
• C. $2.43$
• D. $0.8$

Hint:

When you see $a\log b$ inside an equation, convert it to $\log(b^a)$ and combine logs.

Answer 1

The Correct Option is C

(Logs are base 10.) Move the term to the RHS: \[ \log x=-2+5\log 3=\log\!\big(10^{-2}\big)+\log\!\big(3^5\big)=\log\!\Big(\frac{3^5}{100}\Big). \] Hence \(x=\dfrac{3^5}{100}=\dfrac{243}{100}=2.43.\)