How do you solve the equation #3^(x-1)<=2^(x-7)#?
First, since there are x's in the exponents, we know that we'll be using logs to get those down.
Let's take the natural log of both sides.
In log rules, remember that any exponent inside the log can become the log's coefficient. Or, in math language:
Let's apply that to our equation.
Now, I'm going to factor both sides, because dividing by x wouldn't be very helpful.
Now let's get x on one side of the equation.
And factor the x's
We can use our log rules to simplify.
Then solve for x.
If we further simplify, we find that
Due to the obscure rule
So finally, you get