How to Simplify Logarithmic Equations?

[JakePearson]

i need help with the following quesitons;

a) log_3 27x^2
b) ln (x^2 / y^2)
c) ln (xe^x)
d) log (2x + 3y)

i don't mind if you could direct me in the right direction and i will do my best to go from there :)

USING THE RULES FOR LOGS, SPLIT THE FOLLOWING UP INTO separate LOGARITHM FUNCTIONS AND NUMBERS AS MUCH AS POSSIBLE?

 

[berkeman]

i need help with the following quesitons;

a) log_3 27x^2
b) ln (x^2 / y^2)
c) ln (xe^x)
d) log (2x + 3y)

i don't mind if you could direct me in the right direction and i will do my best to go from there :)

Depends on what x and y are. Could you please provide the full problem statement, and then show us your attempt at the solutions?

 

[HallsofIvy]

First, do you know the "laws of logarithms"?

$log_a(xy)= log_a(x)+ log_a(y)$
$log_a(x^y)= ylog_a(x)$

Also you should know that $log_a(a^x)= x$.

 

[JakePearson]

Using the rules for logs, split the following up into separate logarithm functions and numbers as much as possible?

 

[berkeman]

Using the rules for logs, split the following up into separate logarithm functions and numbers as much as possible?

Okay, so using the hints/review from HallsofIvy, show us your tries at simplifying those equations...