## anonymous one year ago Given the exponential equation 2^x = 8, what is the logarithmic form of the equation in base 10?

1. anonymous

help will medal you

2. anonymous

Do you know how to write 2^x = 8 as a logarithmic equation of base 2?

3. anonymous

i do not

4. anonymous

Exponential and logarithmic forms are just two different ways to write the same equation. For example, we know that $$3^2=9$$. That is the exponential form of the equation. The log from is $$\log_{3} 9=2$$. They mean exactly the same thing. This is how you go from one form to the other |dw:1439501752391:dw|

5. anonymous

See if you can fill in the numbers from your equation |dw:1439501859795:dw|

6. anonymous

oh so it would be log_2=8 ?

7. anonymous

not quite. The 8 should be on the other side of the equation and it looks like you dropped the x|dw:1439501996772:dw|

8. anonymous

oh true so that would equal 3?

9. anonymous

Yes, x does equal 3, but it doesn't look like they want you to solve for it. They want you to rewrite the equation, but keep the x

10. anonymous

It's like a multiple choice question so I have answer choices I can show you if you want to see them

11. anonymous

I don't really need them. Once you have the log equation with base 2 all we have to do is use the change of base formula to convert it to base 10.

12. anonymous

What's the formula you have so far?

13. anonymous

I don't have any right now like I don't know how to do this at all tbh

14. anonymous

I put a graphic up. Follow the arrows to put the numbers/variables in the right place to convert the equation from exponential to logarithmic. Here it is in case you missed it|dw:1439502539460:dw|

15. anonymous

so log_2 8= x and then do we have to solve it or something?

16. anonymous

no. you don't have to solve it

17. anonymous

oh nevermind we dont solve it but what do we do w it?

18. anonymous

we're going to use the change of base formula to convert it to base 10.|dw:1439502646197:dw|

19. anonymous

So you should have $x=\frac{ \log 8 }{ \log 2 }$

20. anonymous

right so do i solve that?

21. anonymous

22. anonymous

oh i have an answer choice that looks like x=log_10 2 divided by log_10 8

23. anonymous

would that be correct?

24. anonymous

no the 8 has to be on top. Is there one that has $x=\frac{ \log_{10} 8 }{ \log_{10}2 }$

25. anonymous

yes! would that be correct?

26. anonymous

Yes That's the same thing as above, except the 10 isn't usually written because it's understood.

27. anonymous

oh okay thank you so much!

28. anonymous

you're welcome