log(3^5) = log(9^2x) ------ use log() to get the exponents out of there...because of the properties of logarithms, it forces the exponents off like this:
log(3) * 5 = log(9) * 2x ------ nice
log(3) * 5 = 2x * log(9) ------------ now divide by log(9)
(log(3) * 5)/log(9) = 2x -------- oh snap, you can see where this is going...
((log(3) * 5))/log(9) ) / 2 = x ------------- divide it all by 2 to get x on its own
x = 5/4
wooo!!!
Note: by default, LOG() is in base ten, even on your calculator. you can do some fancy stuff to change it to a different base, but it seems like youre just learning this so dont worry about that for now.
LOGARITHMS EXPLAINED:
It just means you think about them like this (this first example has no base, so you assume it's base 10):
log(y) = x ...... basically, if 10^x = y is true, and you know what y is, what does x have to be?
It's a problem where they give you a starting number and an answer, but you don't know what the exponent was.
Log of base any other number works like this, too. You are asking the calculator to tell you: what do i have to raise this base number to in order to get the number in the parenthesis?
Comments
3^5 = 9^(2x) ------ starting problem
log(3^5) = log(9^2x) ------ use log() to get the exponents out of there...because of the properties of logarithms, it forces the exponents off like this:
log(3) * 5 = log(9) * 2x ------ nice
log(3) * 5 = 2x * log(9) ------------ now divide by log(9)
(log(3) * 5)/log(9) = 2x -------- oh snap, you can see where this is going...
((log(3) * 5))/log(9) ) / 2 = x ------------- divide it all by 2 to get x on its own
x = 5/4
wooo!!!
Note: by default, LOG() is in base ten, even on your calculator. you can do some fancy stuff to change it to a different base, but it seems like youre just learning this so dont worry about that for now.
LOGARITHMS EXPLAINED:
It just means you think about them like this (this first example has no base, so you assume it's base 10):
log(y) = x ...... basically, if 10^x = y is true, and you know what y is, what does x have to be?
It's a problem where they give you a starting number and an answer, but you don't know what the exponent was.
Log of base any other number works like this, too. You are asking the calculator to tell you: what do i have to raise this base number to in order to get the number in the parenthesis?
Message me if you need more help