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Explain how to solve 4^x+3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

1 Answer

1 vote

The value of x is 1

Step-by-step explanation:

The equation is
4^x+3=7

Subtracting both sides by 3, we get,


4^x=4

Taking log on both sides, we get,


\log 4^(x)=\log 4

Rewriting the equation by
4^(x)=u

Thus, we have,


\log u=\log 4

Applying log rule, if
\log f(x)=\log g(x), then
f(x)=g(x)

Thus,
u=4

Substituting
u=4 in
4^(x)=u, we get,


4^x=4

Also, since,
a^(f(x))=a^(g(x)), then
f(x)=g(x)

Thus,
x=1

Hence, the value of x is 1

User Kishan K
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