Question

How many distinct real solutions exist for x, given log(20x) + log(50x) - 4log(x - 1) = 3?
Please explain ho you figured it out!

Answer 1

i'm assuming all this is log base 10?

Answer 2

Yes. They are all common logarithms.

Answer 3

lol... look at your question... I'm not a ho

Answer 4

lol Sorry. typo. *how :)

Answer 5

\(\large log(20x)+log(50x)-4log(x-1)=3 \)
\(\large log(\frac{(20x)(50x)}{(x-1)^4})=3 \)
\(\large 10^3=\frac{(20x)(50x)}{(x-1)^4} \)
\(\large 10^3=\frac{(1000x^2)}{(x-1)^4} \)
\(\large 1=\frac{(x^2)}{(x-1)^4} \)
\(\large (x-1)^4=x^2 \)
\(\large x^4-4x^3+6x^2-4x+1=x^2 \)
\(\large x^4-4x^3+5x^2-4x+1=0 \)

Answer 6

that last line can be factored as:
\[\large (x^2-3x+1)(x^2-x+1)=0 \]
i guess you can use the quadratic formula for each factor...

Answer 7

Oh, wow! But how did you manage to factor it into the two trinomials?

Answer 8

uh.. mr. wolfram...:)

Answer 9

sorry... i can't factorize into trinomials...

Answer 10

lol. I'm sure I'll figure it out eventually...Thanks though! By the way, how do you get a line underneath the fraction when writing an equation? I can get the forward slash, but not like a fraction.

Answer 11

in this box just use "\[ \
and end it with \]"
without the quotes.

right click this and choose show math as : \[\large \frac{\sqrt{3}}{2}\]

Answer 12

tex commands....

Answer 13

or you can just use the equation button , right next to the draw button at the lower left of this box.

Answer 14

ALright. Thanks! :)

Answer 15

yw...:)