SOLUTION: I'm having some trouble w/ this problem and would appreciate any help: 8^x = 1/128 I came up with this answer: X = 1/ 1024 I'm not sure what I did wrong, but I could use s

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I'm having some trouble w/ this problem and would appreciate any help: 8^x = 1/128 I came up with this answer: X = 1/ 1024 I'm not sure what I did wrong, but I could use s      Log On


   

Question 1040323: I'm having some trouble w/ this problem and would appreciate any help:
8^x = 1/128
I came up with this answer: X = 1/ 1024
I'm not sure what I did wrong, but I could use some help please! Thank you!
Found 4 solutions by josmiceli, addingup, ikleyn, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F128+=+1%2F%28%28+2%5E7%29%29+
+1%2F128+=+2%5E%28-7%29+
--------------------
+8%5Ex+=+2%5E%28-7%29+
+%28+2%5E3+%29%5Ex=+2%5E%28-7%29+
+2%5E%283x%29+=+2%5E%28-7%29+
The exponents have to be equal
+3x+=+-7+
+x+=+-7%2F3+
--------------------
Check the answer:
+8%5Ex+=+1%2F128+
+8%5E%28-7%2F3%29+=+1%2F128+
+8%5E%28-2.3333%29+=+.0078125+
+.007813+=+.0078125+
error due to rounding off

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
8^x = 1/128
:
Take the logarithm base 8 of both sides:
x = (2i*pi*n)/(log(8))-7/3

Answer by ikleyn(52814) About Me  (Show Source):
Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

I'm having some trouble w/ this problem and would appreciate any help:
8^x = 1/128
I came up with this answer: X = 1/ 1024
I'm not sure what I did wrong, but I could use some help please! Thank you!
No, you're incorrect. It appears as though you multiplied the base on the left with the denominator on the right. Can't work!!

8%5Ex+=+1%2F128

%282%5E3%29%5Ex+=+1%2F2%5E7 ------- Substituting matrix%281%2C7%2C+2%5E3%2C+for%2C+8%2C+and%2C+2%5E7%2C+for%2C+128%29

2%5E%283x%29+=+2%5E-+7 ------ Applying matrix%281%2C5%2C+%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29%2C+and%2C+2%5E-7%2C+for%2C+1%2F2%5E7%29

3x = - 7 ---------- Equating exponents since bases are equal

highlight_green%28x+=+-+7%2F3%29