Suppose $log_{5}(11)=b$ Use change-of-base formula & properties of logs to rewrite each expression in terms of a and b. Show the steps for solving.

Screen shot of the exercise I'm working on (exercise 27):

I am able to arrive at an equation of the form $$\frac{1}{b}=...$$

I'd like to check if I'm on the right track and also how to get the expression for a whole $$b$$, not it's reciprocal like I currently have:

My working: $$\log_{11}(5)=\frac{\log_5(5)}{\log_5(11)}$$

Since $$\log_5(11) = b$$: $$\frac{\log_5(5)}{b}=\log_{11}(5)$$ $$\frac{1}{b}=\log_{11}(5)$$

Am I on the right track? How can I express my left hand side as a whole $$b$$ rather than $$\frac{1}{b}$$?

That's completely correct. The questions asks you to write your answer in terms of $$a$$ and $$b,$$ so $$1/b$$ is completely valid. No need to worry that your answer isn't in the form $$kb$$ (or similar). In fact, there's no simpler way to write $$1/b$$ unless I'm missing something.