Question

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

Answer 1

`x = (1)/(log(4))`

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)=(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 = (1)/(log(4))`