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Solve for a Variable in an Exponent

by dein
(Malaysia)











































Find x

(27)^3x+1 = (81)^x-1

1. Convert both sides of the equation to the same base

2. Once both sides of the equation are written with the same base, the exponents will be equal

3. (at this point, ignore the base) Write a separate equation: Set both exponents equal to one another and solve for x.

Comments for Solve for a Variable in an Exponent

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Apr 18, 2011
Algebra – Solve for a Variable in an Exponent
by: Staff


The question:

by Dein
(Malaysia)


Find x

(27)^3x+1 = (81)^x-1


The answer:

(27)^(3x + 1) = (81)^(x – 1)

Convert both side of the equation to base 3

(27)^(3x + 1) = (81)^(x – 1)

(3^3)^(3x + 1) = (3^4)^(x - 1)

3^(9x + 3) = 3^(4x - 4)


Since the bases are the same, the exponents are equal

(9x + 3) = (4x - 4)


Solve for x

9x + 3 = 4x - 4

9x + 3 - 3 = 4x - 4 - 3

9x + 0 = 4x - 4 - 3

9x = 4x - 4 - 3

9x = 4x - 7

9x - 4x = 4x - 4x - 7

9x - 4 x = 0 - 7

9x - 4 x = - 7

5x = - 7

5x/5 = - 7/5

x*(5/5) = - 7/5

x*(1) = - 7/5

x = - 7/5

the final answer is: x = -7/5



Check the work. Substitute -7/5 for x the original equation.



3^(9x + 3) = 3^(4x - 4)

3^(9*(-7/5) + 3) = 3^(4*(-7/5) - 4)

2.62806411 × 10-5 = 2.62806411 × 10-5, correct

Both sides of the original equation equal the same amount when -7/5 is substituted for x.

This verifies that -7/5 is the correct solution.



Thanks for writing.


Staff
www.solving-math-problems.com


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