SOLUTION: if k = log(base7) 9/ log(base 7) 4 then 2^(5k) = I got k = 9/4 but it is wrong! what is K? Thanks in advance!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: if k = log(base7) 9/ log(base 7) 4 then 2^(5k) = I got k = 9/4 but it is wrong! what is K? Thanks in advance!      Log On


   

Question 882228: if k = log(base7) 9/ log(base 7) 4
then 2^(5k) =
I got k = 9/4 but it is wrong! what is K?
Thanks in advance!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Choose use of Change of Base Formula, because we do not typically have tabulated information about logs to base 7.


Choosing Common Logs, base ten:
log%287%2C9%29=log%28%289%29%29%2Flog%28%287%29%29 and log%287%2C4%29=log%28%284%29%29%2Flog%28%287%29%29.

k=%28log%28%289%29%29%2Flog%28%287%29%29%29%2F%28log%28%284%29%29%2Flog%28%287%29%29%29

highlight%28k=log%28%289%29%29%2Flog%28%284%29%29%29.

You can use a table of common logarithms or an electronic calculator for log%28%289%29%29=0.954243 and log%28%284%29%29=0.60206
k=%280.954243%29%2F%280.60206%29=1.5850