Find x using logharitms. 4^(2x-1)-11=0

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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4^(2x-1) -11 = 0

==> 4^(2x-1) = 11

We will apply logarithm for both sides.

==> log 4^(2x-1) = log 11

Now we know that log a^b = b*log a

==> (2x-1)*log 4 = log 11

Now we will divide by log 4

==> 2x-1 = log 11/ log 4

==> 2x = (log11/log4) + 1

==> x = [( log11/log4)+1 ]/ 2 = 1.3649 (aprox)

==> Then the value of x is : x= [ log11/log4) + 1 ]/ 2 = 1.3649 (aprox.)

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation `4^(2x-1)-11=0` has to be solved.

`4^(2x-1)-11=0`

`4^(2x-1) = 11`

Take the logarithm of both the sides.

`log(4^(2x - 1)) = log 11`

Use the relation `log a^b = b*log a`

`(2x -1)*log 4 = log 11`

`2x - 1 = (log 11)/(log 4)`

`2x = (log 11)/(log 4) + 1`

`x = ((log 11)/(log 4) + 1)/2`

The solution of the equation is `x = ((log 11)/(log 4) + 1)/2`

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The first step is to shift 11 to the right side.

4^(2x-1) = 11

Now, to find out x, we'll take log on both sides:

log 4^(2x-1) = log 11

We'll use the power rule of logarithms:

(2x - 1)*log 4 = log 11

We'll divide by log 4 both sides of the equation:

(2x - 1) = log 11 / log 4

We'll add 1  both sides:

2x = (log 11 / log 4) + 1

We'l divide by 2:

x = [(log 11 / log 4) + 1]/2

The solution of the equation is: x = [(log 11 / log 4) + 1]/2.

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