## Write the following expression as a single logarithm with coefficient 1.log910 − log9 12 − log94

### To simplify the expression, we can use the logarithmic identity that states:

log(A) – log(B) = log(A/B)

To simplify the expression, we can use the logarithmic identity that states:

log(A) – log(B) = log(A/B).

Using this identity, let’s simplify the expression step by step.

1. log910 − log9 12 − log94

We can rewrite the expression using the identity mentioned above:

= log(910/12) – log(4)

2. Simplifying the numerator:

The numerator, 910/12, can be simplified further.

910/12 = 75

Therefore, the expression becomes:

= log(75) – log(4)

3. Applying the logarithmic identity again:

Using the identity log(A) – log(B) = log(A/B), we can rewrite the expression as:

= log(75/4)

So, the simplified expression is:

log(75/4) with a coefficient of 1.

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