SOLUTION: CAN YOU PLS TELL ME HOW TO SOLVE LOG 0.3 to the base 9..?? The answer should be 1/2.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: CAN YOU PLS TELL ME HOW TO SOLVE LOG 0.3 to the base 9..?? The answer should be 1/2.       Log On


   

Question 293221: CAN YOU PLS TELL ME HOW TO SOLVE LOG 0.3 to the base 9..??
The answer should be 1/2.
Found 2 solutions by josmiceli, Earlsdon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The main thing to remember is: LOGS ARE EXPONENTS
The other main thing is:
You have to know how to read this:
y+=+log%289%2C.3%29
First of all, it's telling you that y is an exponent,
since it says "y = log(something)"
Then it tells you that when you raise the base 9 to
the exponent y, the result is .3
Putting all that together:
y+=+9%5E.3
You can also express 9 as 3%5E2
y+=+%283%5E2%29%5E.3
The rule for this is to multiply the exponents
y+=+3%5E.6
You can solve this on a calculator, or
take the log to the base 10 of both sides
log%28y%29+=+.6%2Alog%283%29
log%28y%29+=+.6%2A.477
log%28y%29+=+.286
y+=+10%5E.286+
y+=+1.933
-----------------
Actually,
1%2F2+=+log%289%2C3%29
and, as I showed,
1.933+=+log%289%2C.3%29

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Log%5B9%5D%280.3%29+=+x Rewrite this in exponential form:Log%5Bb%5D%28y%29+=+x--->b%5Ex+=+y
9%5Ex+=+0.3 Now take the common log (base = 10) of both sides.
Log%5B10%5D%289%5Ex%29+=+Log%5B10%5D%280.3%29 Use you calculator to find these logs. First apply the power rule for logarithms to the left side.
x%2ALog%289%29+=+Log%280.3%29 Divide both sides by Log%289%29.
x+=+%28Log%280.3%29%29%2FLog%289%29 Use your calculator to find the logs.
x+=+-0.547951637145... Rounded to...
highlight%28x+=+-0.5%29 This does not quite match your answer!