Question

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.

Answer 1

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