Solve please!!

Question

6•3^x-1=18

 

Thank you!

Answer 1

Whenever you see the variable as an exponent, you will probably have to go down the path of isolating the exponential, then taking the log of both sides to get the variable onto the "main line", if you will.

 

6•3^x-1=18

 

step 1: divide both sides by 6

 

3^x-1 = 3

 

step 2: take the log of both sides

log(3^x-1) = log(3)

 

Step 3: recall that log(a^b) = b log(a)

so the left hand side can be transformed to

(x-1)log(3) = log(3)

 

Step 4: divide both sides by log(3)

x-1 = 1

 

Step 5 solve for x

x = 2

 

Confirmation: put 2 into the original equation and see if it works.