SOLUTION: If a=log(base7)(11-6√2) and b=log(base7)(45+29√2), find 3a+2b in the simplest form.
Algebra.Com
Question 253720: If a=log(base7)(11-6√2) and b=log(base7)(45+29√2), find 3a+2b in the simplest form.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
If and , find 3a+2b in the simplest form.
if and only if
if and only if
take log of both sides of first equation to get:
becomes:
this becomes:
divide both sides by log((7)) to get:
*************
take log of both sides of second equation to get:
becomes:
this becomes:
divide both sides by log((7)) to get:
since the denominator is the same, we get:
I don't think you can simplify it any further, but you can solve it using the LOG function of your calculator.
equation becomes:
this becomes:
I confirmed the answer is correct by using the logarithm base conversion formula to convert base 7 logarithm to a base 10 logarithm.
that conversion formula is:
you could also have solved this problem directly by using the base conversion formula.
RELATED QUESTIONS
log base7... (answered by stanbon)
Hi,
I have a maths test tomorrow and i am pretty much sweet except for one thing.... (answered by addingup,ikleyn,MathTherapy)
log(base7)2 times... (answered by Alan3354)
what is the solution set for log [base7] x... (answered by Alan3354)
log(base7)x+log(base7)(x-1)=log(base7)12 (answered by lwsshak3)
Find the sum. Express your answer in simplest form.
(14a^2 / 2b) + (3a / 2b)
a)... (answered by nyc_function)
Find the domain of the logarithmic function. Write your answer in interval notation... (answered by lwsshak3)
PLEASE PLEASE PLEASE PLEASE PLEASE HELP ME.
√(2)[√(4y) - √(18)]... (answered by stanbon)
find the sum. express your answer in simplest form. 14a^2/2b + 3a/2b
a. 14a^2+3a/2b
b.... (answered by scott8148)