Question

Given log a b = x, replace the variables a and b with integers of your choice. (2 points)

Part 2: Show your work to solve the logarithm you created using the change of base formula. (4 points)

Part 3: Provide the solution

Answer 1

So, \(\log_{a}b=x\).
Because you are asking this, I think I may choose the integers :)
So I choose a=3 and b=8:

\(\log_{3}8=x\).

Because 8 is not a "nice" power of 3, we have to change base and use a calculator to solve it.

The rule for changing base is: \(\log_{a}b=x \Leftrightarrow \dfrac{\log_{g}b}{\log_{g}a}=x\).
Read this as follows: the log with base a cannot be found. YOu choose a new base, g, to be able to use a calculator.

On calculators the LOG button, uses log based 10, so we change the base to 10.

This gives us: \(x=\log_{3}8=\dfrac{\log_{10}8}{\log_{10}3}=\dfrac{\log 8}{\log3}\).

Now grab that calculator and see what the solution is!

Answer 2

thank youuuuu! @ZeHanz

Answer 3

YW! 1.892789261