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Verified Answer :

Expand the logarithmic expression. log(base b) sqrt 29/61 

Using the basic log rules:

we get (1/2) [log (base b) 29 - log (base b) 61 ] . 

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Answer:

\(log_b{\sqrt{\frac{29}{61}}=log_b(\sqrt{29}-\sqrt{61}})\)

Step-by-step explanation:

We have been given the expression:

\(log_b{\sqrt{\frac{29}{61}}\)

We will use the property:

\(log_a{\frac{n}{m}}=log_a{m-n}[\)

Here, \(a=b,n=\sqrt{29}\text{and}m=\sqrt{61}\)

So, we will get from the identity:

\(log_b{\sqrt{\frac{29}{61}}=log_b(\sqrt{29}-\sqrt{61})\)

Hence, you are not right because you removed square rrot in final result rest is right.

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