Problem 72
Question
In Exercises \(71-78,\) use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$ \log _{6} 17 $$
Step-by-Step Solution
Verified Answer
The value of \(log_6 17\) to four decimal places, is approximately 1.7654. This uses the change of base formula and a calculator to compute.
1Step 1: Understand the formula to be used - Change of Base Formula
The 'Change of Base Formula' applies to logarithms, which allows changing the base of the logarithm into another number. The formula is \(log_b a = log_c a / log_c b\), where c could be any positive number.
2Step 2: Apply the Change of Base Formula to the given problem
Applying the formula to the given logarithm, we need to find \(log_6 17\), but we only have common logarithms (log) or natural logarithms (ln) on the calculator. Let's use the common logarithm (base 10). The formula then changes to: \(log_6 17 = log 17 / log 6\).
3Step 3: Calculate the values using a calculator
Calculate the values of \(log 17\) and \(log 6\) using a calculator, and then divide the two outputs.
Other exercises in this chapter
Problem 71
Evaluate each expression without using a calculator. $$\ln \frac{1}{e^{6}}$$
View solution Problem 71
The hyperbolic cosine and hyperbolic sine functions are defined by $$\cosh x=\frac{e^{x}+e^{-x}}{2} \quad \text { and } \quad \sinh x=\frac{e^{x}-e^{-x}}{2}$$ P
View solution Problem 72
Explain how to solve a logarithmic equation. Use \(\log _{3}(x-1)=4\) in your explanation.
View solution Problem 72
Evaluate each expression without using a calculator. $$\ln \frac{1}{e^{7}}$$
View solution