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Apply properties of logarithms to solve exponential and logarithmic equations

Apply properties of logarithms to solve exponential and logarithmic equations-example-1
User Thenoseman
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1 Answer

13 votes
13 votes

Given:

Given the equation


\log_3(4-a)=\log_3(-2a+2)

Required: Value of a

Step-by-step explanation:

The given equation can be written as


\log_3(4-a)-\log_3(-2a+2)=0

Use the property


\log_bp-\log_bq=\log_b(p)/(q)

Thus,


\log_3((4-a)/(-2a+2))=0

Take antilogarithm on both sides.


\begin{gathered} (4-a)/(-2a+2)=3^0 \\ 4-a=-2a+2 \\ -a+2a=2-4 \\ a=-2 \end{gathered}

Final Answer: The value of a is -2.

User Fidel Orozco
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