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What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline minus 7 squared) written as a single logarithm?
log Subscript 3 Baseline 2 z
log Subscript 3 Baseline 2 z squared
log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction
log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction

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Answer:

log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction

Step-by-step explanation:

abidemiokin

The single logarithmic form f the expression is [tex]log_3(\frac{9(64z^2)}{81} )[/tex]

Logarithm and indices

Given the logarithmic expression;

[tex]2(log_38+log_3z)-log_3(3^4-7^2)[/tex]

We are to write it as a single logarithm

Using the product and quotient law of logarithm;

[tex]2(log_38+log_3z)-log_3(3^4-7^2)\\=2(log_38+log_3z)-log_3(\frac{81}{49} )\\=2(log_38z)-log(\frac{81}{9})\\=log_364z^2-log(\frac{81}{9})[/tex]

Simplify the final result to have:

[tex]=log_364z^2-log(\frac{81}{9})\\=log_3(\frac{9(64z^2)}{81} )[/tex]

Hence the single logarithmic form f the expression is [tex]log_3(\frac{9(64z^2)}{81} )[/tex]

Learn more on logarithm here: https://brainly.com/question/25710806

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