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

Step 1: Raise \( 10 \) to the power of each side of \( \log x-5\log3=-2 \): \[ 10^{\log x}=10^{-2+5\log3}=10^{-2}\cdot10^{5\log3}. \]

Step 2: Since \( 10^{\log x}=x \) and \( 10^{\log3}=3 \), this becomes \[ x=10^{-2}\cdot3^5=\frac{243}{100}. \]
\[ \boxed{x=2.43} \]