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9 votes
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given that:
log_(2) \: x =a \: and \: log_(2) \: y= b\: therefore ,express
log_(2) {} \: x {}^(2) y \: in \: terms \: of \: a \: and \: b

given that: log_(2) \: x =a \: and \: log_(2) \: y= b\: therefore ,expresslog_(2) {} \: x-example-1
User Ali Abbas
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1 Answer

21 votes
21 votes

GIVEN:

The following values are given:


\begin{gathered} \log _2x=a \\ \log _2y=b \end{gathered}

We are to evaluate:


\log _2x^2y

CALCULATION:

Step 1: Apply the law of logarithm


\log _z(m* n)=\log _zm+\log _zn

Therefore, we have


\log _2x^2y=\log _2x^2+\log _2y

Step 2: Apply the law of logarithm


\log _am^n=n\log _am

Therefore, the first expression becomes:


\log _2x^2=2\log _2x

Hence, the expression becomes:


\Rightarrow2\log _2x+\log _2y

Step 3: Substitute for a and b in the expression above


\begin{gathered} \log _2x=a \\ \log _2y=b \end{gathered}

Therefore, the expression becomes:


2\log _2x+\log _2y=2a+b

ANSWER:


\log _2x^2y=2a+b

User Lenissa
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