SOLUTION: Pls help me. Given that log2^x+log3^81=1 find x?

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Question 1163250: Pls help me. Given that log2^x+log3^81=1 find x?
Found 3 solutions by jim_thompson5910, MathTherapy, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

log%282%2C%28x%29%29+%2B+log%283%2C%2881%29%29+=+1

log%282%2C%28x%29%29+%2B+log%28%2881%29%29%2Flog%28%283%29%29+=+1 Change of base property. Only change log%283%2C%2881%29%29

log%282%2C%28x%29%29+%2B+log%28%283%5E4%29%29%2Flog%28%283%29%29+=+1 Rewrite 81 as 3^4

log%282%2C%28x%29%29+%2B+4%2Alog%28%283%29%29%2Flog%28%283%29%29+=+1 Use the rule that log(x^y) = y*log(x).



log%282%2C%28x%29%29+%2B+4%2Across%28log%28%283%29%29%29%2Fcross%28log%28%283%29%29%29+=+1

log%282%2C%28x%29%29+%2B+4%2A1+=+1

log%282%2C%28x%29%29+%2B+4+=+1

log%282%2C%28x%29%29+=+1-4 Subtracting 4 from both sides

log%282%2C%28x%29%29+=+-3

x+=+2%5E%28-3%29 Convert from log form to exponent form

x+=+1%2F%282%5E3%29

x+=+1%2F8 is the final answer. This is equivalent to 0.125 in decimal form.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Pls help me. Given that log2^x+log3^81=1 find x?
matrix%281%2C3%2C+log+%282%2C+%28x%29%29+%2B+log+%283%2C+%2881%29%29%2C+%22=%22%2C+1%29

Before we go any further, you need to know the value of log+%283%2C+%2881%29%29%29, which we will name c. This gives us: matrix%281%2C3%2C+c%2C+%22=%22%2C+log+%283%2C+%2881%29%29%29
matrix%281%2C3%2C+3%5Ec%2C+%22=%22%2C+81%29%29 ----- Converting to EXPONENTIAL form, based on the RULE: 
matrix%281%2C3%2C+3%5Ec%2C+%22=%22%2C+3%5E4%29
c = 4 ----- BASES are equal and so are the exponents


Continuing, matrix%281%2C3%2C+log+%282%2C+%28x%29%29+%2B+log+%283%2C+%2881%29%29%2C+%22=%22%2C+1%29 now becomes: matrix%281%2C3%2C+log+%282%2C+%28x%29%29+%2B+4%2C+%22=%22%2C+1%29

matrix%281%2C3%2C+x%2C+%22=%22%2C+2%5E%28-+3%29%29 ----- Converting to EXPONENTIAL form

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

Hello,

as I see,  you systematically write your posts  INCORRECTLY;  so they are  UNREADABLE.

If you want to present the formula/expression   log%28b%2Cx%29,

then write in your post   log base b (x).