I need to solve for x and give an exact answer. Exponential equation

Question

5*2^x=70

 

I get this far:

2^x=70/5

 

Answer 1

5*2^x=70

divide both sides by 5

2^x=14

x*log(2)=log(14)

x=log(14)/log(2)

x=1.146128/0.3010299

x=3.807356 (in case you need a specific number answer-as Brad M. said a bit under 4)

Answer 2

5*2^x=70

 

> solve for x and give an exact answer

 

An exact answer means you can't use a calculator. You must find a simplified expression for x.

 

Dividing both sides by 5: 2^x = 14 = 2 * 7

Dividing both sides by 2: 2^(x-1) = 7

Taking log's (base 10) of both sides: log(2^(x-1)) = log(7)

Applying exponent rule for logs: (x-1)log2 = log7

Simplifying: x = ((log7)/(log2)) + 1; which is an exact answer.

 

Answer 3

Hey Adrienne -- since 2^x is 14, then x log 2 = log 14 ... x = log 14 / log 2

~ a bit under 4 for your answer ... All the best, ma'am :)