SOLUTION: write 1+log(base 2) X^3 as a single logarithm. *i dont understand how to do the qustion without changing it into an equation, which would be incorrect. Ex. 1+log(base 2) X^3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: write 1+log(base 2) X^3 as a single logarithm. *i dont understand how to do the qustion without changing it into an equation, which would be incorrect. Ex. 1+log(base 2) X^3       Log On


   



Question 556295: write 1+log(base 2) X^3 as a single logarithm.

*i dont understand how to do the qustion without changing it into an equation, which would be incorrect. Ex. 1+log(base 2) X^3
log(base 2)X^3 = 1 (wrong!)
how would i do it ??

Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
1 = log2(2)

adding logs means multiplying quantities

log2(2) + log2(x^3) = log2(2x^3)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+1+%2B+log%282%2Cx%5E3%29+
The key is to express +1+ in terms of a log
+1+=+log%282%2C2%29+
Make this substitution
+log%282%2C2%29+%2B+log%282%2Cx%5E3%29+
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Now use rule +log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29+
+log%282%2C+2x%5E3%29+ answer
--------------------
I'll check this by setting +x+=+7+ ( or any number )
+1+%2B+log%282%2C7%5E3%29+
+1+%2B+log%282%2C+343%29+
+1+%2B+8.4221++=+9.4221
and
+log%282%2C+2%2A7%5E3%29+
+log%282%2C686%29+=+9.4221+
OK