What is x given that `log_4 (x-5)=-1`

Expert Answers
justaguide eNotes educator| Certified Educator

The value of x has to be determined given that `log_4(x - 5) = -1`

`log_4(x - 5) = -1`

If  `log_a x = b` , `x = a^b`

` `=> `x - 5 = 4^-1`

=> `x = 1/4 + 5`

=> `x = 5.25`

The required value of x is 5.25

baxthum8 eNotes educator| Certified Educator

What is x given `log_(4)(x-5)=-1`

`Log Rule:   `

`log_(x)a = brArr x^b = a`

` 4^-1 = x - 5`

` 1/4 = x - 5 `

`1/4 + 5 = x`

`1/4 + 20/4 = x`

`21/4 = x `

``

Jyotsana | Student

Log4(X-5) =-1

LogCD= a ----- ca= D

X-5=4-1

X-5= 0.25    Add 5 to the both side.

 x-5+5=0.25+5

X=5.25

chhavy | Student

Equation: `log_(4)(x-5) = -1`

To find: value of x

Answer: we will use the following properties:

  1. `x^(-1)=1/x` 
  2. `log_(a)(x)=y``=> x = a^y`

 now from the given equation

`log_(4)(x-5) = -1`

`=> (x-5) = 4^-1`

`=> x-5 = 1/4`

`=> x = 5+(1/4)`

`=> x = 5 + 0.25`

`=> x = 5.25`

` `

PrunTuns | Student

These are two helpful links that may prove useful both presently and in the future (I'm assuming you are just beginning to cover logarithms in class): 

http://www.enotes.com/topics/logarithm-of-a-power

http://www.enotes.com/topics/logarithmic-equations

Wiggin42 | Student

To get rid of the log, we must do the opposite function which is an exponent. Make both sides an exponent with a base for 4. this gets you

x - 5 = 4^-1 = 1/4

Now, you can solve for x just like any other linear function: 

x = .25 + 5

x = 5.25

anzheng | Student

X is equal to 5.25.

4^-1=x-5

1/4=x-5

x=1/4+5

so x is=5.25