Question

Solve 4^x+2=12 for x using the change of base formula logby=logy/logb

Answer 1

Answer:

$x = \frac{1}{log(4)}$

Step-by-step explanation:

Here, the given expression is :

$4^x+2=12$

Now, simplifying the given expression ,we get:

$4^x+2=12 \implies 4^x=12 - 2 = 10\\\implies 4^x = 10$

Now, using the logarithmic property:

$log(b -y)=\frac{log (b)}{log(y)}$

$log(a^m) = m log(a)$

Now, in the expression $4^x = 10$take log on the Both sides, we get:

$4^x = 10 \implies log( 4^x ) = log(10)\\\implies x log(4) = 1$

or, $x = \frac{1}{log(4)}$