Answered

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State the solution in terms of x 4^x+6 = 20

State The Solution In Terms Of X 4x6 20 class=

Sagot :

We have the question as

[tex]4^{x+6}=20[/tex]

Let us introduce logarithms to base 4 to both sides of the equation:

[tex]\log _44^{x+6}=\log _420[/tex]

Applying the law of logarithm that states

[tex]\log A^B=B\log A[/tex]

we have

[tex](x+6)\log _44=\log _420[/tex]

Applying the law that states

[tex]\log _nn=1[/tex]

we have

[tex]\begin{gathered} (x+6)\times1=\log _420 \\ x+6=\log _420 \end{gathered}[/tex]

Collecting like terms, we have

[tex]x=-6+\log _420[/tex]

Therefore, the answer is OPTION C.

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