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Chapter 4: Problem 63
Evaluate each expression without using a calculator. $$\log 10^{7}$$
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In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ \log x+\log 7+\log \left(x^{2}-1\right)-\log (x+1) $$
If \(\ S 4000\) is deposited into an account paying \(3 \%\) interest compounded annually and at the same time \(\ S 2000\) is deposited into an account paying \(5 \%\) interest compounded annually, after how long will the two accounts have the same balance?
In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ \log (2 x+5)-\log x $$
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \ln \left[\frac{x^{3} \sqrt{x^{2}+1}}{(x+1)^{4}}\right] $$
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log \left(\frac{x}{100}\right) $$
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