SOLUTION: -i wasn't sure of how to type in logarithms, i hope you can understand this: -What is the real value of x in the equation log(base=2 argument=24) - log(base=2 argument=3) = log (

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Question 78062: -i wasn't sure of how to type in logarithms, i hope you can understand this:
-What is the real value of x in the equation log(base=2 argument=24) - log(base=2 argument=3) = log (base=5 argument=x)?
-i am preparing for the ACT and we haven't covered logarithms yet. i am trying to learn how to find logarithms, but i still do not understand how to find the value of x.
Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
a logarithm is essentially an exponent...the base, raised to the power of the logarithm, equals the argument

you can find the log of any argument in any base by dividing the log (common or natural) of the argument by the log of the base...sometimes using natural logs (ln) helps avoid confusion

in your case: %28%28ln%2824%29%29%2F%28ln%282%29%29%29-%28%28ln%283%29%29%2F%28ln%282%29%29%29=%28ln%28x%29%29%2F%28ln%285%29%29...using rules for logarithms gives...%28%28ln%2824%2F3%29%29%2F%28ln%282%29%29%29%2A%28ln%285%29%29=ln%28x%29

24/3=8 and since 2^3=8 the first fraction equals 3 giving...3ln(5)=ln(x)...which means 5^3=x...so x=125