Answer:
[tex]x=-1.596[/tex]
Step-by-step explanation:
We want to solve the equation
[tex]4^{(x + 3)} = 7[/tex]
for [tex]x[/tex].
To do that we take the [tex]log_4[/tex] of both sides:
[tex]log_4(4^{(x + 3)}) = log_4(7)[/tex]
[tex]=x+3=log_4(7)[/tex]
For the logarithm on the right side we use the change-of-base formula which says:
[tex]log_b(n)=\frac{log_d(n)}{log_d(b)}[/tex]
For [tex]log_4(7)[/tex] this gives:
[tex]log_4(7)=\frac{log_{10}(7)}{log_{10}(4)}=1.4037[/tex]
Thus we have
[tex]x+3=1.4037[/tex]
[tex]\boxed{\therefore x=-1.596.}[/tex]
