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

7 Answers

baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

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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 `

``

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

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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

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chhavy | (Level 1) eNoter

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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`

` `

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PrunTuns | (Level 1) Honors

Posted on

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's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

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