Re: Logarithm equation
B.P. said:
Log X+Log(X-15)=2 turns into Log X(X-15)=2 which turns into (X-15)=10squared to
Xsq-15X-100=0 to (X+20)(X-5)=0 to X does not equal -5 and X equals 20.
I understand the factoring done in the last three parts but I don't understand why or how they get rid of the log sign and I don't know where they get the 10 squared from.
Ok, here's a tip.
Always keep in mind what people actually mean when they say log(a)=c.
log(a)=c means a=10[sup:148ff2dy]c[/sup:148ff2dy].
So, log(1000)=3 means 1000=10[sup:148ff2dy]3[/sup:148ff2dy]
And log(0.1)=-1 means 0.1=10[sup:148ff2dy]-1[/sup:148ff2dy]
And log(1)=0 means 1=10[sup:148ff2dy]0[/sup:148ff2dy]
And log(2)=0.30103... means 2=10[sup:148ff2dy]0.30103...[/sup:148ff2dy]
You are given : log(X(X-15)) = 2.
But log(X(X-15))=2 means X(X-15)=10[sup:148ff2dy]2[/sup:148ff2dy]
That's how they get rid of the log, and that's where the 10[sup:148ff2dy]2[/sup:148ff2dy] came from.
Later, your teacher will introduce logs to other bases. log[sub:148ff2dy]b[/sub:148ff2dy]a=c means a=b[sup:148ff2dy]c[/sup:148ff2dy]. So, log[sub:148ff2dy]3[/sub:148ff2dy]81=4, because 81=3[sup:148ff2dy]4[/sup:148ff2dy] and so on. But you don't need that for this problem...
