Express as a single logarithm. Simplify as much as possible.
11+4ln(6x-10)-10ln(5x+1)
I got:
11+ln ((6x-10)^4/(5x+1)^10)
thank you again
correct, but why do you exclude the 11?
ln (e^11 (6x-10)^4/(5x+1)^10)
could you look at another problem I already posted..no matter what I put in , it says wrong
see:
www.jiskha.com/questions/1873850/express-as-sums-differences-and-multiples-of-logarithms-expand-as-much-as-possible
thank you Oobleck
the correct question is
ln(x^14√x+15/(12x−2)^15)
there is no parentheses in the numerator. It reads like this:
x^14√x+15 thank you!
To express the given expression as a single logarithm, you need to simplify the terms and combine them into one logarithm.
Starting with the given expression: 11 + 4ln(6x-10) - 10ln(5x+1)
To simplify the terms, we can apply logarithmic properties:
1. The power property of logarithms states that log base b of a^c is equal to c multiplied by log base b of a.
Using this property, we can simplify 4ln(6x-10) to ln((6x-10)^4).
2. Similarly, -10ln(5x+1) can be simplified to ln((5x+1)^(-10)). Applying the power property of logarithms, the exponent -10 can be moved from the front of the logarithm to the inside as a reciprocal exponent.
Now we can rewrite the expression with the simplified terms:
11 + ln((6x-10)^4) - ln((5x+1)^10)
To combine these terms into a single logarithm, we can use the quotient rule of logarithms. According to the quotient rule, log base b of a minus log base b of c is equal to log base b of (a/c).
Applying the quotient rule, we can rewrite the expression as:
11 + ln(((6x-10)^4)/((5x+1)^10))
So, the given expression simplified and expressed as a single logarithm is:
11 + ln(((6x-10)^4)/((5x+1)^10))