solve 2(5^x)-1=15

Question

solve for x. if the answer is not an integer, enter it as a decimal rounded to the nearest hundredth if needed

Answer 1

Philip is silly. You don't need to have multiple logs, let alone natural logs.

 

 

He got you to 5^x = 8, which is correct, but from there, just use the definition of log:

 

log_b(m) = a   <===>   b^_a = m

 

 

Your equation matches with the structure of the right side; b=5, a=x, m=8. Put those into the left side, and you get log₅(8) = x.

 

Then just put that into your calculator to find the answer. Much easier :)

 

 

If you have any questions, just let me know!

Answer 2

2*5^x - 1 = 15

 

2*5^x = 16

 

5^x = 8

 

ln(5^x) = ln(8)

 

Using the identity ln(a^b) = b*ln(a):

 

x*ln(5) = ln(8)

 

x = ln(8)/ln(5)

 

Use your calculator to compute the answer.