SOLUTION: solve for x x= 6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64) I am not sure how to find X, I would appreciate if someone can help me.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for x x= 6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64) I am not sure how to find X, I would appreciate if someone can help me.       Log On


   

Question 998682: solve for x
x= 6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64)
I am not sure how to find X, I would appreciate if someone can help me. I will provide my step.
x=6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64)
=6/8 (log(base6) sqrt(108)/ (2/sqrt3) + log(base 6) 9^2 + log(base6) 64)
=6/8 (log(base6) sqrt(108) / (2/sqrt3) + log(base 6) (81)(64)
=6/8 (log(base6) 9 + log(base6) 5184)

=6/8 (log(base6) (9)(5184)
=6/8 (log(base6) 46656)
= log(base6) 34992

Found 3 solutions by mananth, MathTherapy, greenestamps:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
x= log(base6) 34992

6^x = 34 992 ⇒ x = 5.839

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
solve for x

x= 6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64)

I am not sure how to find X, I would appreciate if someone can help me. I will provide my step.

x=6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64)

 =6/8 (log(base6) sqrt(108)/ (2/sqrt3) + log(base 6) 9^2 + log(base6) 64)

 =6/8 (log(base6) sqrt(108) / (2/sqrt3) + log(base 6) (81)(64)

 =6/8 (log(base6) 9 + log(base6) 5184)
 
 =6/8 (log(base6) (9)(5184)

 =6/8 (log(base6) 46656)

 = log(base6) 34992
*******************




x+=+%286%2F8%29%28log+%286%2C+%28sqrt%28108%29%28sqrt%283%29%2F2%29%29%2881%29%2864%29%29%29

x+=+%286%2F8%29%28log+%286%2C+%28sqrt%28108%29sqrt%283%29%2881%29%2832%29%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%28sqrt%28108%2A3%29%2881%29%2832%29%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%28sqrt%28324%29%2881%29%2832%29%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%2818%2A81%2A32%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%2818%2A81%2A16%2A2%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%2818%2A2%2A81%2A16%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%2836%2A81%2A16%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%286%5E2+%2A+9%5E2+%2A+4%5E2%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%286%5E2+%2A+%289%2A4%29%5E2%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%286%5E2+%2A+36%5E2%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%286%5E2+%2A+%286%5E2%29%5E2%29%29%29
x+=+%286%2F8%29%28log+%286%2C+%286%5E2%29%5E3%29%29
x+=+%286%2F8%29%28log+%286%2C+%286%5E6%29%29%29
x+=+log+%286%2C+%286%5E6%29%5E%286%2F8%29%29
matrix%282%2C1%2C+%22+%22%2C+x+=+log+%286%2C+%286%5E%2836%2F8%29%29%29%29

matrix%282%2C1%2C+%22+%22%2C+x+=+log+%286%2C+%286%5E%289%2F2%29%29%29%29
highlight%28x%29+=+highlight%289%2F2%29 ---- Applying log+%28b%2C+%28b%5Ec%29%29+=+c

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


solve for x
x= 6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64)
I am not sure how to find X, I would appreciate if someone can help me. I will provide my step.
x=6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + log(base6) 64)
=6/8 (log(base6) sqrt(108)/ (2/sqrt3) + log(base 6) 9^2 + log(base6) 64)
=6/8 (log(base6) sqrt(108) / (2/sqrt3) + log(base 6) (81)(64)
=6/8 (log(base6) 9 + log(base6) 5184)
=6/8 (log(base6) (9)(5184)
=6/8 (log(base6) 46656)
= log(base6) 34992

------------------------------------------------------------------

Your work is fine up to the last step.

It will be easier to find the answer if you leave the expression in factored form instead of multiplying all the numbers together.

The entire expression is of the form

(6/8) (... extended expression in a form equivalent to "log (base6) of A")

Let's drop all the "log (base 6)" notations and just look at the "A". Using basic log rules, A is as follows:

%28%28sqrt%28108%29%29%289%5E2%29%2864%29%29%2F%282%2Fsqrt%283%29%29

Performing basic arithmetic WITHOUT multiplying all the numbers together....

%286sqrt%283%29%29%289%5E2%29%2864%29%28sqrt%283%29%2F2%29

%286%29%283%29%289%5E2%29%2832%29

And now remembering that we are looking for the value of the log base 6 of this number....

%286%29%283%29%283%5E4%29%282%5E5%29=%286%29%283%5E5%29%282%5E5%29=%286%29%286%5E5%29=6%5E6

Finally, then....

x=%286%2F8%29log%286%2C%286%5E6%29%29=%283%2F4%29%286%29=9%2F2

ANSWER: 9/2