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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