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solve exponential equationfind x if 8^(6x+5)-2/8=0

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colorcolour | Student, College Freshman | (Level 1) Honors

Posted April 29, 2011 at 7:04 AM via web

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solve exponential equation

find x if 8^(6x+5)-2/8=0

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted April 30, 2011 at 9:50 AM (Answer #2)

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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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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 30, 2011 at 10:26 AM (Answer #3)

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The equation to be solved is 8^(6x+5)-2/8=0

8^(6x+5) = 2/8

=> 2^3^(6x + 5) = 1/4 = 2^-2

As the base 2 is the same, equate the exponent

3*(6x + 5) = -2

18x + 15 = -2

=> 18x = -17

=> x = -17/18

The value of x = -17/18

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