What is x if 8^(6x+5)=1/4 ?

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hala718's profile pic

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

Posted on

8^(6x+5) = 1/4

Let us rewrite the numbers.

We know that"

8 = 2^3

1/4 = 1/2^2 = 2^-2.

Let us substitute into the equation.

==> (2^3)^(6x+5) = 2^-2.

Now we know that x^a^b = x^ab

==> 2^(3(6x+5) = 2^-2.

==> 2^(18x+15) = 2^-2.

Now that we have the bases equal, then the powers should be equal.

==> 18x + 15 = -2.

Now we will subtract 15 from both sides.

==> 18x = -2 -15

==> 18x = -17

Now we will divide by 18 both sides;

==> x= -17/18

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write 8 and 4 as powers of 2:

2^3(6x+5) = 1/2^2

We'll apply the rule of negative power:

1/a^b = a^-b

2^3(6x+5) = 2^-2

Since the bases are matching, we'll apply one to one rule and we'll put equal the exponents.

3(6x+5) = -2

We'll remove the brackets:

18x + 15 + 2 = 0

We'll combine like terms:

18x + 17 = 0

We'll subtract 17 and we'll divide by 18:

x = -17/18

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