Question

Find the exact solution to the equation.

10-log4(x+6) = 9

Please Show steps. I dont know what to do when there is a log on just one side of the equation

Answer 1

Exact solution to the equation is 10-log4(x+6) = 9 is -2

Step-by-step explanation:

As we have given the logarithm equation in the question that

`10-log4(x+6)=9` ……….(1)

Now by using the logarithm property, we know that

x+6>0

So x>-6

Now from equation 1

`log4(x+6)=1`

As we know the anti log property as
`loga(x)=b` then it becomes
`(x)=(a)^b`

Now by using anti log Properties, the above equation would becomes

`x+6=(4)^1`

`x+6=(4)`

`x=-6+(4)`

So x=-2

Hence the possible value of x that satisfy the given logarithm equation is -2.