Determine the solutionDetermine the solution of the equation log 4 (2x-20) = 1

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to substitute for 1 such that:

Since the bases are equal, then you need to equate the numbers such that:

Factoring out 2 yields:

Hence, evaluating the solution to the given equation yields x = 12.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve log(4) (2x-20) = 1

log(4) (2x-20) = 1

=> 2x - 20 = 4^1

=> 2x = 20 + 4

=> 2x = 24

=> x = 12

The solution of the equation is x = 12

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Before solving the equation, we have to impose constraints of existance of logarithm function.

2x-20>0

We'll add 20 both sides:

2x>20We'll divide by 2:

x>10

So, for the logarithms to exist, the values of x have to be in the interval (10, +inf.)

Now, we'll solve the equation:

2x-20= 4^1

2x-20 = 4

We'll add 20 both sides:

2x = 20+4

2x = 24

We'll divide by 2:

x = 12

The solution is admissible because the value belongs to the interval (10,+inf.)

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