Solve the equation log 4 (x-8) = 2 .

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hala718's profile pic

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

Posted on

log 4 (x-8) = 2

We know that if log a (b) = c  ==> b= a^c

==> x-8 = 4^2

==> x-8 = 16

==> x= 16+8

==> x= 24

Let us check:

log 4 (x-8) = 2

log 4 (24-8) =2

log 4 (16) = 2

==> 16 = 4^2

==> 16 = 16

Top Answer

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.

x-8>0

We'll add 8 both sides:

x>8

So, in order to exist, the values of x have to be in the interval (8, +inf.)

Now, we'll solve the equation:

x-8 = 4^2

x-8 = 16

We'll add 8 both sides:

x = 16+8

x = 24

The solution is admissible because is in the interval (8,+inf.).

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve log4 (x-8) = 2.

Solution

log4(x-8) = 2.  But RHS = 2 = log 4 (4^2)

log4 (x-8) = log4 (4^2) . Take antilog.

x-8 = 4^2 = 16

x =  16+8 =24.

x

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