Homework Help: Solve log 3 log10 y = -2

DeanBH · May 11, 2008

how do logs work when it's like this.

3 log10 y = -2

log10 y = a
10^a = y

so it's 10^-2 = y

but where does the 3 go, and why does it go there. i'm not sure.

rocomath · May 11, 2008

FFR (for future reference) :p ln is base e and log by itself, is implied base 10.

Power Rule: [tex]\log y^3=-2 \leftrightarrow 3\log y=-2[/tex]

Logarithmic to Exponential form: [tex]\log_a B=m \leftrightarrow a^m=B[/tex]

DeanBH · May 11, 2008

so

3logy = -2
logy^3 = -2
log10^-2 = y^3
y=10^(-2/3)

rocomath · May 11, 2008

Your third line is wrong, but your final answer is correct. I'm not sure what you were doing, but you wouldn't take the log of the right side then drop the log on the left.

HallsofIvy · May 11, 2008

Another way to do that problem is to just divide both sides by 3 at the start:
3 log y= -2 so log y= -2/3. Now, the example you showed says that y= 10^-2/3 as before.

DeanBH · May 12, 2008

rocomath said: ↑

Your third line is wrong, but your final answer is correct. I'm not sure what you were doing, but you wouldn't take the log of the right side then drop the log on the left.

should be 10^-2 = y^3 without log?

cristo · May 12, 2008

rocomath said: ↑

ln is base e and log by itself, is implied base 10.

Whilst your first point is always true, your second point is not. I know people (myself included) who sometimes write log(x) to be base e. One should always check the conventions of the book that one is using.