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

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) (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:
=
Multiply both sides by 27, gets rid of both denominators:

; exponent equivalent of Square Root is 1/2
Use nat logs:
;
Use log equiv of exponents
;
:

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 =
x = +.857
:
:
Check solution using calc
enter: = .0593
and
= .0593 also, confirms our solution of x=.857
:
:
(B) (cubedsqrt4/2)^6x=2sqrt2
On the 2nd one is this what you mean?
=
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:

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 =
x = -.74998 ~ -.75 is what it is:
:
Check this using a calc
Find the value of 6x: -.75*6 = -4.5
enter: = 2.8284
enter: = 2.8284 also confirms our solution x = -.75
:
Did this make sense to you, Any questions?

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