Algebra Question

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1. Write the inverse function off\left(x\right)=\log_5x?

2. What is the last step for solving a logarithmic equation? 

3. Simplify: LaTeX: 2^{\log_2}\left(\sqrt{7}\right).

4. What is the first thing you do to solve the given exponential equation  2^x=24 ?

Write the first step that you do.

5. What is the first step that needs to be done to solve \log_4x+\log_4\left(x-3\right)=1\: ? Write the first step.

6. True or false?

LaTeX: \log\left(x.y\right)=\log x.\log ylog⁡(x.y)=log⁡x.log⁡y

If false, write the above equation with correction

7. What is the change of base formula? Or write a formula for LaTeX: \log_aMloga⁡M.

8. Write as a single logarithm.  LaTeX: 2\log x+3\log y2log⁡x+3log⁡y.

9. Simplify: LaTeX: \ln e^{t^{ }}ln⁡et.

10. Simplify LaTeX: \log\left(\frac{1}{10^k}\right)log⁡(110k). (Hint: Use rule LaTeX: \frac{1}{x^m}=x^{-m}1xm=x−m)

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