Algebra Exponential and Sums & Difference of Logarithmic Questions

Algebra Exponential and Sums & Difference of Logarithmic Questions

1. Determine whether the given functions are one-to-one. It they are one-to-one, find a formula for the inverse.(a)
   $f\left(x\right)=-x+5$(b)
   $f\left(x\right)=x^2-4$(c)
   $f\left(x\right)=2x^3-5$(d)
   $f\left(x\right)=\sqrt{x-5}$(e)
   $f\left(x\right)=\frac{6}{x+5}$
2. Answer the following exponential and logarithmic questions(a) Use properties of logarithms to expand the logarithmic expression,
   $\log \left(10,000x^2\right)$ Then simplify.(b) Solve the equation
   $3^x=81$(c) Solve the equation
   ${\log }_6\left(x+2\right)=2$(d) Express in terms of sums and difference of logarithms
   ${\log }_b\left(6x^{5}y{z}^2\right)$(e) Expand and simplify

Maybe one or two problems on graphing

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