SOLUTION: This is the first time my instructor has presented problems written this way. I'm clueless. I would appreciate if someone could show me how to do this one so I can handle the rest.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: This is the first time my instructor has presented problems written this way. I'm clueless. I would appreciate if someone could show me how to do this one so I can handle the rest.      Log On


   

Question 192060: This is the first time my instructor has presented problems written this way. I'm clueless. I would appreciate if someone could show me how to do this one so I can handle the rest. Thank you
If a is a positive real number, such that a is not equal to 1, and ax = b,
then the logarithmic function is represented as:
A) log a^x b = x
B) loga^b = f(a^x)
C) log b = x= a^x
D) loga^b = x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If "a" is a real number and a%5Ex=b, we can isolate "x" by applying the logarithm base 10 to both sides to get log%2810%2C%28a%5Ex%29%29=log%2810%2C%28b%29%29.


From there, pull down the exponent "x" to get x%2Alog%2810%2C%28a%29%29=log%2810%2C%28b%29%29



Now divide both sides by log%2810%2C%28a%29%29 to get x=log%2810%2C%28b%29%29%2Flog%2810%2C%28a%29%29


Combine the terms on the right side (using the change of base formula) to get x=log%28a%2C%28b%29%29


So after isolating "x", we get x=log%28a%2C%28b%29%29


Note: it turns out that b%5Ey=x <====> log%28b%2C%28x%29%29=y. In other words, we can convert to and from exponential and logarithmic form.