Mathematics: How can the logarithmic expression be rewritten? select true or false for each statement.

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How can the logarithmic expression be rewritten? select

Ответ:

hunterthompson2

12.01.2022

Mathematics

1. log_3(cd)^4 = 4 log_3(c )+ log_3(d) FALSE

$2. \frac{2}{3} (ln(a) +ln(b)) = ln(\sqrt[3]{a^2b^2} )$ TRUE

$3.ln(\frac{e^3}{f} ) = 3 ln(e) - ln (f)$ TRUE

Step-by-step explanation:

Here, let us first state the logarithmic rules.

$log (a) - log (b) =log(\frac{a}{b} )\\log (ab) = log a + log b\\log(a^m) = m \times log (a)$

Now, here the given expressions are:

1. log_3(cd)^4 = 4 log_3(c )+ log_3(d)

The given statement is FALSE as:

log_3(cd)^4 = 4 log_3(cd) = 4log_3(c) + 4log_3(d)

$2. \frac{2}{3} (ln(a) +ln(b)) = ln(\sqrt[3]{a^2b^2} )$

$\frac{2}{3} (ln(a) +ln(b)) = \frac{2}{3} ln(ab) = ln(ab) ^\frac{2}{3} \\= ln(\sqrt[3]{a^2b^2} )\\\implies\frac{2}{3} (ln(a) +ln(b)) = ln(\sqrt[3]{a^2b^2} )$

The given statement is TRUE .

$3.ln(\frac{e^3}{f} ) = 3 ln(e) - ln (f)$

The given statement is TRUE as:

$ln(\frac{e^3}{f} ) = ln(e^3) - ln (f) = 3 ln(e) - ln (f)$

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How can the logarithmic expression be rewritten? select true or false for each statement.

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