Solve log4(x-6)= -1
Where do you start?
Your first step would be to remove the log.
If log(x) = y
Then x = 10^y
(I'm assuming the log in the question is base 10)
I will assume you mean:
log4(x-6)= -1
then ..
x-6 = 4^-1
x-6 = 1/4
4x-24 = 1
4x = 25
x = 25/4
To solve the logarithmic equation log4(x-6) = -1, we need to rewrite it in exponential form.
The logarithmic equation log4(x-6) = -1 can be written as 4^(-1) = x - 6.
Now, let's simplify the left side of the equation:
4^(-1) = 1/4
So, we have 1/4 = x - 6.
To isolate x, we can add 6 to both sides of the equation:
1/4 + 6 = x
Multiplying 1/4 and 6, we get:
6/4 + 6 = x
Simplifying the left side, we have:
3/2 + 6 = x
Adding the fractions, we get:
(3 + 12)/2 = x
Therefore, x = 15/2 is the solution to the equation log4(x-6) = -1.