If log x-5log3=-2, then x equals:

1955 AMC 12 Problem 17

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17.

\log x-5\log3=-2,

then

x

equals:

1.25

0.81

2.43

0.8

either

0.8

1.25

Move

5\log3

to the other side

Use

-2=\log10^{-2}

and combine logarithms

Using common logarithms,

\begin{aligned} \log x&=5\log3-2\\ &=\log(3^5)-\log100\\ &=\log\left(\frac{243}{100}\right). \end{aligned}

Therefore

x=2.43.

The correct answer is C.