Question

express the logarithm​

Answer 1

Answer:

Suppose that:

log10A=a

log10B=b

log10C=c

I need to express the following in terms of a,b,c.

log10A+2log10(1/A)

log10(((AB)5)/C)

log10((100A2)/(B4⋅C−−√3))

Step-by-step explanation:

Remember your laws of logs:

log10(XY)=log10(X)+log10(Y)

log10(X/Y)=log10(X)−log10(Y)

log10(XY)=Y⋅log10(X)

So for the first one: log10(A)+2⋅log10(1/A) =log10(A)+2⋅log10(A−1) =log10(A)−2⋅log10(A) =−log10(A)=−a

Alternatively: log10(A)+2⋅log10(1/A) =log10(A)+2⋅log10(1)−2⋅log10(A)=a+2⋅0−2a=−a (because log(1)=0)