SOLUTION: Need to solve the following - PLEASE HELP!!! 1. 4x^3/4 = 108 (exponent is 3/4) Also - this one is weird to write 2. e^x * 4e ^2x+1 (the 2x+1 are all in superscript/e

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Need to solve the following - PLEASE HELP!!! 1. 4x^3/4 = 108 (exponent is 3/4) Also - this one is weird to write 2. e^x * 4e ^2x+1 (the 2x+1 are all in superscript/e      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 93276: Need to solve the following - PLEASE HELP!!!
1. 4x^3/4 = 108 (exponent is 3/4)
Also - this one is weird to write
2. e^x * 4e ^2x+1 (the 2x+1 are all in superscript/exponents)
And one more - tough to write
3. 5^ x-1 = 125^2x+3 ( the x-1 and 2x+3 are exponents/superscript)
THANKS THANKS
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
1. 4x^3/4 = 108 (exponent is 3/4)
4x%5E%283%2F4%29+=+108
x%5E%283%2F4%29+=+27
x+=+27%5E%284%2F3%29
x+=+%283%5E3%29%5E%284%2F3%29
x+=+%283%29%5E%283%2A4%2F3%29
x+=+3%5E4
x+=+81
2. e^x * 4e ^2x+1 (the 2x+1 are all in superscript/exponents)
e%5Ex+%2A+4e%5E%282x+%2B+1%29
4%28e%5Ex+%2A+e%5E%282x+%2B+1%29%29
4e%5E%28x+%2B+2x+%2B+1%29
4e%5E%283x+%2B+1%29
3. 5^ x-1 = 125^2x+3 ( the x-1 and 2x+3 are exponents/superscript)
5%5E%28x+-+1%29+=+125%5E%282x+%2B+3%29
5%5E%28x+-+1%29+=+%285%5E3%29%5E%282x+%2B+3%29
5%5E%28x+-+1%29+=+5%5E%283%282x+%2B+3%29%29
5%5E%28x+-+1%29+=+5%5E%286x+%2B+9%29
x+-+1+=+6x+%2B+9
-10+=+5x
-2+=+x

Answer by stanbon(48569) About Me  (Show Source):
You can put this solution on YOUR website!
1. 4x^3/4 = 108 (exponent is 3/4)
Raise both sides to the (4/3) power to get:
4^(4/3)x = 108
x = 108/[4^(4/3)]
x = 108/6.349604208...
x = 17.00893417...
-----------------
2. e^x * 4e ^2x+1 (the 2x+1 are all in superscript/exponents)
This is not an equation; no equal sign.
--------------
3. 5^ x-1 = 125^2x+3 ( the x-1 and 2x+3 are exponents/superscript)
5^(x-1) = 125^(2x+3)
5^(x-1) = (5^3)^(2x+3)
5^(x-1) = 5^(6x+9)
x-1 = 6x+9
5x = -10
x = -2
=================
Cheers,
Stan H.