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

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