Check the solution to "Write each expression as a sum and/or difference..."

BolkowN

Answered question

2021-08-14

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
1)

\log_{5} (25 x)

\log_{3} \frac{x}{9}

\log_{2} z^{3}

bahaistag

Skilled2021-08-15Added 100 answers

1) Given:

\log_{5} (25 x)

since

∣ \log_{c} (a b) = \log_{c} (a) + \log_{c} (b)

therefore

\log_{5} (25 x) = \log_{5} (25) + \log_{5} (25)

and we have

\log_{5} (25) = 2

so,

\log_{5} (25 x) = 2 + \log_{5} x

2) Given:

\log_{3} \frac{x}{9}

since we have

\log_{c} \frac{a}{b} = \log_{c} (a) - \log_{c} (b)

therefore

\log_{3} \frac{x}{9} = \log_{3} (x) - \log_{3} (9)

\log_{3} (9) = 2

\log_{3} \frac{x}{9} = \log_{3} (x) - 2

3) Given:

\log_{2} z^{3}

we have

\log_{c} m^{n} = n \log_{c} m

then

\log_{2} z^{3} = 3 \log_{2} z

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