Question

Solve the equation. log(x+7) - logx=3

Answer 1

Hint :
\[\large \log( a) - \log (b) = \log \left(\frac{a}{b}\right)\]

Answer 2

The first step like Ganeshie has stated is to combine the 2 logarithmic functions. Can you attempt to use Ganeshie's hint?

Answer 3

no, i dont understand were i need to plug in the numbers

Answer 4

what do you know about logs ?

Answer 5

not much really

Answer 6

thats good because we can start fresh :)

Answer 7

`logs` are same as `exponents`

you might be knowing that \(2\times 2\times 2\) equals \(8\) and we write it in short form as :
\[\large 2^3 = 8\]

Answer 8

another way to write the same thing is :
\[\large \log_2 8 = 3\]

Answer 9

oh okay

Answer 10

let me ask you a question

Answer 11

write below in log form :
\[\large 3^4 = 81\]

Answer 12

\[\log _{3}81= 4\]

Answer 13

no?

Answer 14

Perfect!

Answer 15

Lets look at our original problem.
Applying the first property,
\[\log(x+7) - \log x=3\]

becomes
\[\log\left(\frac{x+7}{x}\right)=3\]

Answer 16

Btw, the default base is \(10\) :

\[\log_{10}\left(\frac{x+7}{x}\right)=3\]

changing this to exponent form you get :
\[\frac{x+7}{x} = 10^3\]

Answer 17

\[\frac{x+7}{x} = 1000\]

Answer 18

\[x+7 = 1000x\]

isolate \(x\)