Evaluate the logarithm. Round your answer to the nearest thousandth. log_(8)(500)~~

Understand the Problem: Understand the problem. We need to find the value of the logarithm of 500 with base 8, which is written as log₈(500). This means we are looking for the power to which we must raise 8 to get 500.Use Change of Base Formula: Use the change of base formula. The change of base formula allows us to write log₈(500) in terms of logarithms with a base that our calculator can handle (usually base 10 or base e). The formula is: log₈(500) = log(500) / log(8)Calculate with Calculator: Calculate the value using a calculator. Using a calculator, we find: log(500) ≈ 2.69897 log(8) ≈ 0.90309 Now we divide these two values to find log₈(500). log₈(500) ≈ 2.69897 / 0.90309Perform the Division: Perform the division. Dividing the two values we get: log₈(500) ≈ 2.98831Round the Answer: Round the answer to the nearest thousandth. Rounding 2.98831 to the nearest thousandth gives us: log₈(500) ≈ 2.988

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Evaluate the logarithm.
Round your answer to the nearest thousandth.

log_(8)(500)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{8}(500) \approx$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

Q. Evaluate the logarithm.

\newline

Round your answer to the nearest thousandth.

\newline

\log _{8}(500) \approx

Understand the Problem: Understand the problem. $\newline$ We need to find the value of the logarithm of $500$ with base $8$ , which is written as $\log_8(500)$ . This means we are looking for the power to which we must raise $8$ to get $500$ .
Use Change of Base Formula: Use the change of base formula. $\newline$ The change of base formula allows us to write $\log_8(500)$ in terms of logarithms with a base that our calculator can handle (usually base $10$ or base $e$ ). The formula is: $\newline$ $\log_8(500) = \frac{\log(500)}{\log(8)}$
Calculate with Calculator: Calculate the value using a calculator. $\newline$ Using a calculator, we find: $\newline$ $\log(500) \approx 2.69897$ $\newline$ $\log(8) \approx 0.90309$ $\newline$ Now we divide these two values to find $\log_8(500)$ . $\newline$ $\log_8(500) \approx \frac{2.69897}{0.90309}$
Perform the Division: Perform the division. $\newline$ Dividing the two values we get: $\newline$ $\log_8(500) \approx 2.98831$
Round the Answer: Round the answer to the nearest thousandth. $\newline$ Rounding $2.98831$ to the nearest thousandth gives us: $\newline$ $log_8(500) \approx 2.988$