Resolved: "Write the following expression as a sum and/or..."

CoormaBak9

Answered question

2021-08-05

Write the following expression as a sum and/or difference of logarithms. Express powers as factors.

\log_{d} (u^{8} v^{3}) u > 0, v > 0

\log_{d} (u^{8} v^{3}) = ?

(Simplify your answer.)

AGRFTr

Skilled2021-08-06Added 95 answers

Step 1
It is required to write the expression as a sum or difference of logarithms.
The given expression is:

\log_{d} (u^{8} v^{3})

Step 2
Use property:

\log_{d} (a \cdot b) = \log_{d} (a) + \log_{d} (b)

Step 3
Now, apply the above property to simplify:

\log_{d} (u^{8} v^{3}) = \log_{d} (u^{8}) + \log_{d} (v^{3})

Step 4
Now use the property:

\log_{d} (x^{n}) = n \log_{d} (x)

Step 5
By applying the property expression reduces to:

\log_{d} (u^{8} v^{3}) = \log_{d} (u^{8}) + \log_{d} (v^{3})

\log_{d} (u^{8} v^{3}) = 8 \log_{d} (u) + 3 \log_{d} (v)

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