Scelta multipla
Rewrite the log expression as a sum of multiple logs. Further simplify if possible.
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13. Inverse, Exponential, & Logarithmic Functions
Properties of Logarithms
Scelta multipla
Rewrite the sum as a single logarithm. Further simplify if possible.
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Recall the logarithm property that states: \(\log_b A + \log_b B = \log_b (A \times B)\). This means when you add two logarithms with the same base, you can rewrite them as the logarithm of the product of their arguments.
Identify the two logarithms given: \(\log_5 \frac{1}{3}\) and \(\log_5 12y\). Since both have the same base 5, you can apply the property directly.
Multiply the arguments inside the logarithms: \(\frac{1}{3} \times 12y\). This will give you the new argument inside a single logarithm.
Simplify the product \(\frac{1}{3} \times 12y\) by performing the multiplication: multiply the numerator 1 by 12y and divide by 3.
Write the final expression as a single logarithm with base 5: \(\log_5\) of the simplified product from the previous step.
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