SOLUTION: Solve the indicial linear equation 5√8^2x=128^x X 64

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Question 1198055: Solve the indicial linear equation 5√8^2x=128^x X 64
Found 3 solutions by Alan3354, ankor@dixie-net.com, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the indicial linear equation 5√8^2x=128^x X 64
----------------
Not clear.
What is under the radical? 8? 8^2? 8^(2x)?
----
Use * (shift 8) for multiply, not X.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the indicial linear equation 5√8^2x=128^x X 64
:
5sqrt%288%5E%282x%29%29=128%5Ex+%2A+64
rewrite this using exponents
5%2A%288%5E%282x%29%29%5E%281%2F2%29+=+128%5Ex+%2A+64
5%2A%288%5E%282x%2A%281%2F2%29%29%29+=+128%5Ex+%2A+64
cancel the 2
5%2A%288%5Ex%29+=+128%5Ex+%2A+64
put what we can into base 2
5%2A%282%5E%283x%29%29+=+2%5E%287x%29+%2A+64
5%2F64+=+2%5E%287x-3x%29
5%2F64+=+2%5E%284x%29
write it
2%5E%284x%29+=+5%2F64
4x*ln(2) = ln(5/64)
4x = ln%285%2F64%29%2Fln%282%29
4x = -3.678
x = %28-3.678%29%2F4
x = -.9195


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the indicial linear equation 5√8^2x=128^x X 64
    matrix%281%2C3%2C+5sqrt%288%5E%282x%29%29%2C+%22=%22%2C+128%5Ex+%2A+64%29
matrix%281%2C3%2C+5sqrt%28%282%5E3%29%5E%282x%29%29%2C+%22=%22%2C+%282%5E7%29%5Ex+%2A+64%29 ------ Changing 8 and 128 to base 2
     ------- Applying matrix%281%2C3%2C+%28a%5Eb%29%5Ec%2C+%22=%22%2C+a%5E%28bc%29%29
 ------- Applying 
   matrix%281%2C3%2C+5%282%5E%283x%29%29%2C+%22=%22%2C+2%5E%287x%29+%2A+64%29 ------- Applying matrix%281%2C3%2C+%28a%5Eb%29%5Ec%2C+%22=%22%2C+a%5E%28bc%29%29
         matrix%281%2C3%2C+5%2F64%2C+%22=%22%2C+2%5E%287x%29%2F2%5E%283x%29%29 
         matrix%281%2C3%2C+5%2F64%2C+%22=%22%2C+2%5E%284x%29%29 --- Applying matrix%281%2C3%2C+a%5Eb%2Fa%5Ec%2C+%22=%22%2C+a%5E%28b+-+c%29%29
         matrix%281%2C3%2C+4x%2C+%22=%22%2C+log%282%2C+%285%2F64%29%29%29 ----- Converting to LOGARITHMIC form
         matrix%281%2C3%2C+4x%2C+%22=%22%2C+log%28%285%2F64%29%29%2Flog%28%282%29%29%29 ====> matrix%281%2C3%2C+x%2C+%22=%22%2C+%28log%28%285%2F64%29%29%2Flog%28%282%29%29%29%2F4%29 =====>