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Solve the following logarithms. Write your solution in exact form, simplified if possible.

Solve the following logarithms. Write your solution in exact form, simplified if possible-example-1
User Eadmaster
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1 Answer

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Recall that:


\log _bx=a\text{ if and only if }x=b^a.

Therefore:


\log _5(5-2x)=3\text{ if and only if }5-2x=5^3.

Simplifying the above equation we get:


5-2x=125.

Adding 2x to the above equation we get:


\begin{gathered} 5-2x+2x=125+2x, \\ 5=125+2x, \end{gathered}

Subtracting 125 from the above equation we get:


\begin{gathered} 5-125=125+2x-125, \\ -120=2x\text{.} \end{gathered}

Finally, dividing by 2 we get:


\begin{gathered} -(120)/(2)=(2x)/(2), \\ -60=x\text{.} \end{gathered}

Answer: x= -60.

User MhFarahani
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