Step by step solution to "Use common logarithms to find the value of..."

Answered question

2022-04-21

Use common logarithms to find the value of y in y=(1.08)^15

nick1337

Expert2023-04-29Added 777 answers

We are given the equation

y = (1.08)^{15}

and we need to find the value of

y

using common logarithms.
Taking the logarithm of both sides with base 10, we get:

\log_{10} y = \log_{10} (1.08)^{15}

Using the exponent rule of logarithms, we can bring the exponent out in front of the logarithm:

\log_{10} y = 15 \log_{10} 1.08

We can then evaluate

\log_{10} 1.08

using a calculator:

\log_{10} 1.08 \approx 0.033423

Substituting this value back into the equation, we get:

\log_{10} y \approx 15 (0.033423)

Simplifying, we get:

\log_{10} y \approx 0.501345

To solve for

y

, we can take the antilogarithm (or inverse logarithm) of both sides with base 10:

y \approx 10^{0.501345}

Using a calculator, we get:

y \approx 3.040

Therefore, using common logarithms, the value of

y

y = (1.08)^{15}

is approximately

3.040

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