The value of x is 1
Explanation:
The equation is [tex]4^x+3=7[/tex]
Subtracting both sides by 3, we get,
[tex]4^x=4[/tex]
Taking log on both sides, we get,
[tex]\log 4^{x}=\log 4[/tex]
Rewriting the equation by [tex]4^{x}=u[/tex]
Thus, we have,
[tex]\log u=\log 4[/tex]
Applying log rule, if [tex]\log f(x)=\log g(x)[/tex], then [tex]f(x)=g(x)[/tex]
Thus, [tex]u=4[/tex]
Substituting [tex]u=4[/tex] in [tex]4^{x}=u[/tex], we get,
[tex]4^x=4[/tex]
Also, since, [tex]a^{f(x)}=a^{g(x)}[/tex], then [tex]f(x)=g(x)[/tex]
Thus, [tex]x=1[/tex]
Hence, the value of x is 1
