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Screen shot of the exercise I'm working on (exercise 27): enter image description here

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 $\frac{1}{b}$?

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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.

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