a.

First, write the logarithm as an equation.


Next, write the logarithmic equation as an exponential equation.



Two to what exponent will give «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»32«/mn»«/mstyle»«/math»?

b.

First, recall that a radical can be written as a power.


Now, rewrite the logarithm as an equation.


Write the logarithmic equation as an exponential equation.


Express the equation with the like base of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»9«/mn»«/mstyle»«/math», and simplify.


If the bases are the same value, the exponents must be equal for the equation to be true.

a.

Write the logarithmic equation as an exponential equation.

b.

Write the logarithmic equation as an exponential equation.


Write the base of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math» as a power raised to a power. (Think backwards. A power raised to a power would have the exponents multiplied.)


Now, solve for «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math». Take the square root of both sides of the equation.


Logarithms cannot have negative bases, so the negative solution, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mstyle»«/math», is ignored. This will be further discussed in the following section.

Now, cube both sides of the equation.