Answer:
[tex]x = \frac{1}{log(4)}[/tex]
Step-by-step explanation:
Here, the given expression is :
[tex]4^x+2=12[/tex]
Now, simplifying the given expression ,we get:
[tex]4^x+2=12 \implies 4^x=12 - 2 = 10\\\implies 4^x = 10[/tex]
Now, using the logarithmic property:
[tex]log(b -y)=\frac{log (b)}{log(y)}[/tex]
[tex]log(a^m) = m log(a)[/tex]
Now, in the expression [tex]4^x = 10[/tex]take log on the Both sides, we get:
[tex]4^x = 10 \implies log( 4^x ) = log(10)\\\implies x log(4) = 1[/tex]
or, [tex]x = \frac{1}{log(4)}[/tex]
