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# Solve the fallowing: (A) `logsqrt(7)(5x-1)-logsqrt(7)(x+7)=0` (B)   `3x^(x+4)=6` (C)...

ranger1980 | Student, Undergraduate | Valedictorian

Posted October 26, 2013 at 8:20 PM via web

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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`

Tagged with elementary functions, math

### 1 Answer |

tiburtius | High School Teacher | (Level 3) Associate Educator

Posted October 26, 2013 at 8:59 PM (Answer #1)

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(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`

(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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