## coolaidd 3 years ago solve. then round answer to the nearest hundredth. 6^x-3=52

1. coolaidd

|dw:1342135467157:dw|

2. dpflan

\[6^{x-3} = 52\]You will need to use logarithms to solve this one

3. dpflan

Specifically, you will need to use the property of logarithms such that will allow you to work with the exponent: So, if you have \[x^y\], if you take the log of this you obtain: \[log_a(x^y) = y * log_a(x)\]The exponent now becomes a factor in the product

4. dpflan

For your equation, you will want to take the logarithm of both sides, then you can solve for x. You can use any base for the logarithm: \[log_a\] I'm sure you're familiar with the concept of logarithms, but here is nice way to remember what it does: you can say that when you have the expression: \[log_ab = x\]You are looking for the number you raise 'a' to in order to obtain 'b' is 'x'. \[a^x = b\] \[log_28=3\]The number you raise 2 to in order to obtain the value 8, is 3. \[2^3 = 8\]

5. dpflan

Does this seem familiar or helpful?

6. coolaidd

yes..

7. dpflan

8. coolaidd

thanks

9. dpflan

Do you think you can solve this problem?

10. coolaidd

log_5 x=3 x = 5^3 = 125

11. coolaidd

sorry!

12. coolaidd

6^(x - 3) = 52 (x - 3) ln 6 = ln 52 x - 3 = ln 52/ln 6 x = 3 + ln 52/ln 6 ≈ 5.20523

13. dpflan

Yeah, nice!

14. coolaidd

thanks! :)

15. dpflan

Sure, good luck with the rest of your studies! Maybe you can help with some questions even ;)