Question

Chapter 5:Indices and Logarithms
Solve the following equation.
@ganeshie8

Answer 1

\[\log _{10}50+2\log _{10}x-\log _{10}(x+4)=2\]

Answer 2

aren't you forgetting the other two?
square the numerator x--right? in the two steps before

Answer 3

oh

Answer 4

\[\log _{10}(\frac{ 50(x^2) }{ x+4 })=2\]

Answer 5

\[\frac{ 50x^2 }{ x+4 }=100\]

Answer 6

\[50x^2=400x+400\]

Answer 7

\[50x^2-400x-400=0\]

Answer 8

\[50(x^2-8x-8)=0\]

Answer 9

\[50(x-8)(x+1)=0\]

Answer 10

\[x=8,-1\]

Answer 11

After this step
log[50(x^2)/(x+4)]=2
why did you multiply each side by 50?

I would have used e

Answer 12

Ecellent! but `log` can only digest positive numbers
since you have a term \(\log_{10}(x)\) in your original given equation, you need to throw away the solution \(x=-1\)

Answer 13

so the answer is only x=8? @ganeshie8

Answer 14

Yep!

Answer 15

that's what he's saying
but can you explain my question on your question?

Answer 16

@adamaero is right, there is a mistake after below step :

\[\frac{ 50x^2 }{ x+4 }=100\]

Answer 17

Thnx @ganeshie8 and @adamaero

Answer 18

wolfram says x=4 is the only solution
http://www.wolframalpha.com/input/?i=solve+%5Clog_%7B10%7D+50%2B2%5Clog_%7B10%7Dx-%5Clog_%7B10%7D%28x%2B4%29%3D2+over+reals

Answer 19

\[\frac{ 50x^2 }{ x+4 }=100\]

cross multiplying gives u
\[50x^2=100(x+4)\]

Answer 20

cancel 50 both sides and work the remaining quadratic

Answer 21

x=4 and x=-2

Answer 22

yes throw away -2 because it makes the expression \(\log_{10}(x)\) unreal..

Answer 23

Thnx @ganeshie8 :D