Question

current learning objective: using the definition of a logarithm to s
question 38 practice similar questions
score: 0 of 1 point
solve the equation 16\log_{10}(3x) = 5 for x.
x = enter your answer
(round to 3 decimal places if necessary).

Explanation:

Step1: Isolate the logarithm

Divide both sides of the equation \(16\log_{10}(3x) = 5\) by \(16\).
\(\log_{10}(3x)=\frac{5}{16}\)

Step2: Use the definition of a logarithm

By the definition of a common logarithm (\(\log_{a}b = c\) implies \(b=a^{c}\), here \(a = 10\)), we have \(3x=10^{\frac{5}{16}}\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x=10^{\frac{5}{16}}\) by \(3\).
\(x=\frac{10^{\frac{5}{16}}}{3}\)
Now, calculate \(10^{\frac{5}{16}}\):
\(10^{\frac{5}{16}}=e^{\frac{5}{16}\ln(10)}\approx e^{\frac{5\times2.302585}{16}}\approx e^{0.719558}\approx2.054\)
Then \(x=\frac{2.054}{3}\approx0.685\)

Answer:

\(x\approx0.685\)