SOLUTION: Please help with the following: If logb5 = 2 and logb7 = 3, find the value of the following expression : logb35b^4 Thank you for your help!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help with the following: If logb5 = 2 and logb7 = 3, find the value of the following expression : logb35b^4 Thank you for your help!      Log On


   

Question 858985: Please help with the following: If logb5 = 2 and logb7 = 3, find the value of the following expression : logb35b^4
Thank you for your help!
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
log%28b%2C5%29=2 and log%28b%2C7%29=3 as given.
Find log%28b%2C%2835b%5E4%29%29.

log%28b%2C%2835b%5E4%29%29=log%28b%2C%285%2A7%2Ab%5E4%29%29_____|____factoring the argument
log%28b%2C5%29%2Blog%28b%2C7%29%2Blog%28b%2Cb%5E4%29______|____logarithm of a product
log%28b%2C5%29%2Blog%28b%2C7%29%2B4%2Alog%28b%2Cb%29______|____logarithm of number raised to a power
Using the given statements,
2%2B3%2B4log%28b%2Cb%29_____________|_____substitution of given information
5%2B4%2A1____________________|______Exponential and logarithm functions are inverses
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