SOLUTION: Solve:(A) (1/27)sqrt3^x=81(^x-1)/9 (B) (cubedsqrt4/2)^6x=2sqrt2 I am worried that I have not typed (B) correctly but if someone could even help me with(A) I would appreciat

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve:(A) (1/27)sqrt3^x=81(^x-1)/9 (B) (cubedsqrt4/2)^6x=2sqrt2 I am worried that I have not typed (B) correctly but if someone could even help me with(A) I would appreciat      Log On


   

Question 126382: Solve:(A) (1/27)sqrt3^x=81(^x-1)/9
(B) (cubedsqrt4/2)^6x=2sqrt2
I am worried that I have not typed (B) correctly but if someone could even help me with(A) I would appreciate it .
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:(A) (1/27)sqrt3^x=81(^x-1)/9
OK, it should look this then:
%281%2F27%29sqrt%283%5Ex%29 = %2881%5E%28x-1%29%29%2F9
Multiply both sides by 27, gets rid of both denominators:
sqrt%283%5Ex%29+=+3%2881%5E%28x-1%29%29
3%5E%28x%2F2%29+=+3%2881%5E%28x-1%29%29; exponent equivalent of Square Root is 1/2
Use nat logs:
ln%283%5E%28x%2F2%29%29+=+ln%283%29+%2B+ln%2881%5E%28x-1%29%29;
Use log equiv of exponents
%28x%2F2%29%2Aln%283%29+=+ln%283%29+%2B+%28x-1%29%2Aln%2881%29;
:
%28x%2F2%29%2A%281.0986%29+=+1.0986+%2B+%28x-1%29%2A%284.3944%29
Divided 2 into 1.0986
.5493x = 1.0986 + 4.3944x - 4.3944
:
.5493x = 4.3944x - 3.2958
:
.5493x - 4.3944x = -3.2958
:
-3.8451x = -3.2958
x = %28-3.2958%29%2F%28-3.8451%29
x = +.857
:
:
Check solution using calc
enter: %281%2F27%29sqrt%283%5E.857%29 = .0593
and
%2881%5E%28.857-1%29%29%2F9 = .0593 also, confirms our solution of x=.857
:
:
(B) (cubedsqrt4/2)^6x=2sqrt2
On the 2nd one is this what you mean?
%28cubeRt%284%29%2F2%29%5E%286x%29 = 2sqrt%282%29
Use a calc to find cube root of 4 divided by 2: enter 4^(1/3)/2 = .7937
Use a calc to find the square root of 2 times 2: enter 2^(1/2)*2 = 2.8284
now we have:
.7937%5E%286x%29+=+2.8284
Find the nat log of both sides, use the log equiv of exponents
6x * ln(.7937) = ln(2.8284)
:
6x * -.23105 = 1.0397
:
-1.3863x = 1.0397; multiplied by 6
x = 1.0397%2F%28-1.3863%29
x = -.74998 ~ -.75 is what it is:
:
Check this using a calc
Find the value of 6x: -.75*6 = -4.5
enter: %284%5E%281%2F3%29%2F2%29%5E%28-4.5%29 = 2.8284
enter: 2sqrt%282%29 = 2.8284 also confirms our solution x = -.75
:
Did this make sense to you, Any questions?