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Solve the equation to find the value of x. log2(5x-4)=4

Solve The Equation To Find The Value Of X Log25x44 class=

Sagot :

The given equation is

[tex]\log _2(5x-4)=4[/tex]

To solve for x, the logarithm to indices relationship will be applied

That is

[tex]\begin{gathered} \log _ab=x \\ \Rightarrow b=a^x \end{gathered}[/tex]

Hence

[tex]\begin{gathered} \log _2(5x-4)=4 \\ \Rightarrow5x-4=2^4 \end{gathered}[/tex]

This is simplified to get

[tex]\begin{gathered} 5x-4=16 \\ 5x=16+4 \\ 5x=20 \\ x=\frac{20}{5} \\ x=4 \end{gathered}[/tex]

Therefore, the value of x = 4

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