91Ó°ÊÓ

Trisha said that the equation \(5^{x}+6=127\) could be solved by writing the logarithmic equation \(x \log 5+\log 6=\log 127 .\) Do you agree with Trisha? Explain why or why not.

In \(3-14,\) solve each equation for the variable. Express each answer to the nearest hundredth. $$ 12+9^{x}=122 $$

In \(15-23,\) evaluate each logarithm to the nearest hundredth. $$ \log 80 $$

The decay constant of francium is \(-0.0315\) minutes. a. After how many minutes will 1.25 grams of francium remain of a 10.0 -gram sample? Assume the exponential decay occurs continuously. b. What is the half-life of francium? (The half-life of an element is the length of time needed for half of a sample to decay. For example, it is the length of time for a sample of 10 grams to be reduced to 5 grams of the original element.)

In \(11-22,\) solve each equation for \(y\) in terms of \(x\) $$ x=\log _{8} y $$

In \(15-26,\) write each logarithmic equation in exponential form. $$ -2=\log _{5} 0.04 $$

Write each expression as a single logarithm. \(\log _{e} x+2 \log _{e} y-2 \log _{e} z\)

Expand each expression using the properties of logarithms. \(\log _{3} \frac{10}{x}\)

Expand each expression using the properties of logarithms. \(\log _{10}(x+1)^{2}\)

In \(53-56,\) find each value of \(x\) to the nearest thousandth. $$ e^{x}=35 $$