solve the logarithmic equation round to the nearest then-thousandth if necessary
3 \log_{ 10 }({ 2x }) = 4
To solve the logarithmic equation:
3 \log_{ 10 }({ 2x }) = 4
We can first divide both sides by 3 to isolate the logarithm:
\log_{ 10 }({ 2x }) = \frac{4}{3}
The logarithmic equation can be rewritten in exponential form as:
10^{\frac{4}{3}} = 2x
Now, we can solve for x by dividing both sides by 2:
x = \frac{10^{\frac{4}{3}}}{2}
Using a calculator, we can evaluate this expression to find the approximate value of x. Round to the nearest thousandth:
x ≈ 3.17