If lg x = m and lg y = n, express (xy) in terms of m and n. (common log.)?

[solar]

Please can you explain step by step beacsue I am not able to solve this particular problem.

[RayS]

logx = m
logy = n

logx + logy = m + n added and
log(xy) = m+n Used log rule ... logM + logN = logMN
xy = 10 by definition of logarithm ... logu = v u = a
where u=xy, a=10, and v=(m+n)

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[mathie]

Remember what log means.
10^m=x
10^n=y
xy=10^m * 10^n=10^(m+n)

[casey]

First, just for your own edification, it's log, not lg; anyway:

We first write out the logarithms in a simple manner:
log(x) = m
log(y) = n

As we want to isolate x and y to multiply together, we raise both sides to 10^:
10^(log(x)) = 10^m
10^(log(y)) = 10^n

We can simplify from here: 10^log will cancel, leaving x or y:
x = 10^m
y = 10^n

Now, we multiply these together:
x*y = (10^m)*(10^n)
x*y = 10^(m+n)

There you go. Hope that helps.