SOLUTION: If log_b 2 = x and log_b 3 = y, evaluate the following in terms of x and y: (a) log_b 432 = (b) log

SOLUTION: If log_b 2 = x and log_b 3 = y, evaluate the following in terms of x and y: (a) log_b 432 = (b) log_b 162 =

Question 370846: If log_b 2 = x and log_b 3 = y, evaluate the following in terms of x and y:
(a) log_b 432 =
(b) log_b 162 =
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

In order to rewrite an expression in terms of x and y, given the above, we will need to find a way to rewrite 432 and 162 in terms of 2's and 3's. Prime factorization will help:

So
Now we can use a property of logarithms, , to split the argument giving us:

Next we can use another property of logarithms, , to move the exponent of each argument out in front:

And last of all we replace the two logarithms with x and y respectively:
4*(x) + 3*(y)
or
4x+3y

Repeating all of the steps above for the other logarithm:

RELATED QUESTIONS
If log base b of 2 =x and log base b of 3 = y, evaluate the following terms of x and y: (answered by ikleyn)

If log (subscript b)M=x and log (subscript b)N=y, express the following in terms of x and (answered by user_dude2008,stanbon)

if log base b (2)=x and log base b (3)=y, evaluate the following terms of x and y: log (answered by stanbon)

Let a= log x, b = log y and c = log z Write log (x^2 root y/z^3) in terms of a, b and c (answered by jim_thompson5910)

If log a^2 b^3 = x and log (a/b) = y, what are the values of log a and log... (answered by josmiceli)

if log 2 = a; log 3 = b express log 15 in terms of a and b (answered by Alan3354)

if log 2 = a; log 3 = b express log 150 in terms of a and... (answered by josgarithmetic,MathLover1,Alan3354,ikleyn,MathTherapy)

If A=log 2 and B=log 3, write the following in terms of A and B: a)log 36 b)log 54 (answered by stanbon)

a. rewrite the expression in terms of log x and log y. log(x^4y^3) B. rewrite the... (answered by stanbon)