Get the solution to "Express in terms of logarithms of x, y,..."

Nadia Clayton

Answered question

2022-04-04

Express in terms of logarithms of x, y, z, or w.

\log_{4} (x z)

Jonathon Hanson

Beginner2022-04-05Added 9 answers

Step 1
Given logarithmic expression is

\log_{4} (x z)

.
To express logarithms in terms of

x, y, z

w

.
Solution:
We know that,

\log (m n) = \log m + \log n

Therefore,

\log_{4} (x z)

can be written as:

\log_{4} (x z) = \log_{4} x + \log_{4} z

Step 2
From property of logarithm, we have

\log_{a} b = \frac{\log b}{\log a}

And if we have

\log x

, it means it's base is 10.
Therefore, above expression can be further simplified as:

\log_{4} (x z) = \log_{4} x + \log_{4} z

= \frac{\log x}{\log 4} + \frac{\log z}{\log 4}

= \frac{1}{\log 4} [\log x + \log z]

Hence,

\log_{4} (x z) = \frac{1}{\log 4} [\log x + \log z] .

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