Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic
expressions.

(Type an exact answer in simplified form. Use integers or
ractions for any numbers in the expression.)

Ask by Brewer Peterson. in the United States

Mar 23,2025

Question

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic
expressions.

(Type an exact answer in simplified form. Use integers or
ractions for any numbers in the expression.)

Ask by Brewer Peterson. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

We begin with the given expression:
$$
\log_{3} 405 - \log_{3} 5
$$
Using the logarithm property
$$
\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right),
$$
we can combine the logs:
$$
\log_{3} 405 - \log_{3} 5 = \log_{3} \left(\frac{405}{5}\right).
$$
Simplify the fraction:
$$
\frac{405}{5} = 81,
$$
so the expression becomes:
$$
\log_{3} 81.
$$
Now, since $$ 81 = 3^4 $$, we have:
$$
\log_{3} 81 = \log_{3} 3^4.
$$
By applying the power rule of logarithms:
$$
\log_b \left(b^k\right) = k,
$$
we obtain:
$$
\log_{3} 3^4 = 4.
$$
Thus, the condensed logarithmic expression is:
$$
\log_{3} 405 - \log_{3} 5 = 4.
$$
$$ \log_{3} 405 - \log_{3} 5 = 4 $$

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic
expressions.

(Type an exact answer in simplified form. Use integers or
ractions for any numbers in the expression.)

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Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. (Type an exact answer in simplified form. Use integers or ractions for any numbers in the expression.)

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Latest Algebra Questions

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic
expressions.

(Type an exact answer in simplified form. Use integers or
ractions for any numbers in the expression.)