Question

If $\log 2=0.3010$ and $\log 3=0.4771,$ the value of $x$ when $3^{x+3}=135$ is approximately:

$5$

$1.47$

$1.67$

$1.78$

$1.63$

Answer: B

Concepts:logarithm exponent estimation

Difficulty rating: 1340

Small Hint:

Divide by $3^3$ to obtain $3^x=5$

Big Hint:

Use $\log5=1-\log2$ and divide by $\log3$

Solution:

The equation reduces to $3^x=5,$ so $\begin{aligned} x&=\frac{\log5}{\log3}\\ &=\frac{1-\log2}{\log3}\\ &=\frac{0.6990}{0.4771}\\ &\approx1.47. \end{aligned}$

Thus, the correct answer is B.

1954 AMC 12 Problem 38

Answer: B

Difficulty rating: 1340

Small Hint:

Big Hint:

Solution:

Problem 38 in Other Years