91Ó°ÊÓ

In Exercises \(83-88,\) let \(\log _{b} 2=A\) and \(\log _{b} 3=\) C. Write each expression in terms of \(A\) and \(C\). $$ \log _{b} 6 $$

Solve each logarithmic equation in Exercises \(49-92 .\) Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$ \log (x+7)-\log 3=\log (7 x+1) $$

Make Sense? In Exercises \(83-86,\) determine whether catch statement makes sense or does not make sense, and explain your reasoning. I'm using a photocopier to reduce an image over and over by \(50 \%,\) so the exponential function \(f(x)-\left(\frac{1}{2}\right)^{x}\) models the new image size, where \(x\) is the number of reductions.

Solve each logarithmic equation in Exercises \(49-92 .\) Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$ 2 \log x-\log 7=\log 112 $$

Exercises \(83-85\) will help you prepare for the material covered in the first section of the next chapter. $$\text { Solve: } 5(2 x-3)-4 x-9$$

I'm using a photocopier to reduce an image over and over by \(50 \%,\) so the exponential function \(f(x)-\left(\frac{1}{2}\right)^{x}\) models the new image size, where \(x\) is the number of reductions. I'm looking at data that show the number of new college programs in green studies, and a linear function appears to be a better choice than an exponential function for modeling the number of new college programs from 2005 through 2009 .

In Exercises \(83-88,\) let \(\log _{b} 2=A\) and \(\log _{b} 3=\) C. Write each expression in terms of \(A\) and \(C\). $$ \log _{b} 8 $$

Evaluate or simplify each expression without using a calculator. $$ 10^{\log 33} $$

Evaluate or simplify each expression without using a calculator. $$ 10^{\log 53} $$

Solve each logarithmic equation in Exercises \(49-92 .\) Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$ \log (x-2)+\log 5=\log 100 $$