Solve the fallowing:

(A) `logsqrt(7)(5x-1)-logsqrt(7)(x+7)=0`

(B) `3x^(x+4)=6`

(C) `4+3IN(x) = 5`

(D) `3 x^(2+x)-9 x^(2-3)=0`

### 1 Answer | Add Yours

**(A)**

`logsqrt7(5x-1)-logsqrt7(x+7)=0`

Now we use the following `log(x/y)=logx-logy.`

`log((sqrt7(5x-1))/(sqrt7(x+7)))=0`

` ` `log((5x-1)/(x+7))=0`

Now we use the following `logx=0=>x=1`

`(5x-1)/(x+7)=1`

`5x-1=x+7`

`4x=8`

`x=2` **<--Your solution**

**(B)**

This can only be solved numerically and approximate solution is `xapprox1.144`

**(C)**

What does `IN` mean?

**(D)**

This equation can only be solved numerically and approximate solution is `xapprox1.292` ` `

When trying to find numerical solution you can use many different methods, but since these are differentiable and monotonically increasing functions probably the fastest method would be Newton-Raphson method.

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