Discrete Mathematics
posted by Joy .
If f(x) = log2 (x  2)3 and g(x) = log8 (x  2), when is (f + g)(x) = 0?

working with logs base 2,
since 8=2^3, g(x) = 1/3 log(x2)
(f+g)(x) = f(x)+g(x)
= 3log(x2) + 1/3 log(x2)
= 10/3 log(x2)
so, if (f+g)(x) = 0,
log(x2) = 0
x2 = 1
x = 3
check
log_2(32)^3 = 0
log_8(32) = 0 
Thanks Steve! I am starting to write these down so that way I will understand them. It is easier for me to go off an example. I appreciate all your help.
Respond to this Question
Similar Questions

College Algebra
I REALLY don't understand the reason/basis/use of logarithms. I have listened to my teacher, who never is clear on much of anything (it would help if he spoke better English), and a more advanced student, who couldn't explain them … 
Logarithms
I'm working on logarithmic equations and I'm stuck on how my book arrives at the next step. First, they use the change of base formula on, log(sqrt(2))(x^3  2) (sqrt(2)) is the base,changing to base 2 log(sqrt(2))(x^3  2)= log2(x^3 … 
math
solve the equation log2(x+4)log4x=2 the 2 and 4 are lower than the g This is what I got: log2(x+4)+log2(4^x)=2 log2((x+4)*4^x)=2 4^x(x+4)=4 x=0 is a solution? 
Math
The problem I have to solve is log with base 2 ^6 multiply by log base 6 ^ 8. I use the change of base formula and got log6/log2 * log8/log6 Which become log6/log2 * log2()^3/ log 6 I'm stuck here thanks. 
Discrete Math
There are 150 students taking Discrete Mathematics II, Calculus II, and Physics I courses. Of these 51 are taking Discrete Mathematics II, 111 are taking Calculus II, and 63 are taking Physics I. There are 41 taking Discrete Mathematics … 
Math
Hello! Could someone please take a look at the problem below and let me know if I made mistakes in simplifying the given equation? 
Math
I don't understand how log2 √(1/2) turned into log2 2^(1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A  logk B 3. logk (A^n) = n logk A where k is any positive … 
Math
I don't understand how log2 √(1/2) turned into log2 2^(1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A  logk B 3. logk (A^n) = n logk A where k is any positive … 
Math
I don't understand how log2 √(1/2) turned into log2 2^(1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A  logk B 3. logk (A^n) = n logk A where k is any positive … 
Urgent math
i need help with these two homework problems Use the Laws of Logarithms to combine the expression into a single logarithm log2 5 − 5 log2 x + 1/2 log2(x + 1) Solve the logarithmic equation for x log2(x + 2) + log2(x − 1) …