Posted by Michael on Saturday, January 29, 2011 at 7:34pm.
We note that the base of the powers are related to 2, for example, 8=2³, and (1/16)=2-4.
8^(6x-3)=(1/16)^(5x-9)
(2³)^(6x-3) = (2-4)^(5x-9)
Apply the laws of exponentiation,
2^(3(6x-3))=2^(-4(5x-9))
Take log to the base 2 on both sides:
3*(6*x-3)=-4*(5*x-9)
Solve for x to get 45/38.
8^(6x - 3) = (1/16)^(5x - 9),
(2^3)^(6x - 3) = (1/2^4)^(5x - 9),
(2^3)^(6x - 3) = (2^-4)^(5x - 9),
2^(18x - 9) = 2^(-20x + 36),
18x - 9 = -20x + 36,
18x + 20x = 36 + 9,
38x = 45,
x = 45 / 38 = 1.184.
Related Questions
Math help! - I dont understand this. Solve -5x - 6 = -6x^2 Rearrange to 6x^2-5x-...
Math - Can someone please check my answers below for accurateness? The ...
algebra - what is a quartic function with only the two real zeros given x=5 and ...
math - Multiplying and Dividing Rational Expressions: 2) x^2-8x+7/x^2+6x-7 = (x-...
math - Multiplying and Dividing Rational Expressions: 2) x^2-8x+7/x^2+6x-7 = (x-...
algebra - How do you solve 1/16=64^(5x-4)? thank you Notice that 16 and 64 are ...
maths - solve the following simultaneous equation: 5x+2y=29 x-y=-4 2x-y=-1 3x-y=...
math/algebra1a - Write the equation of the line passing through (-3, -5)and (3,0...
algerbra 1 - 5x+8+3x-x+5=6x-3 do I start like this 5x+3x-x or 5x+3x+8+5=6x-3 I ...
Find the sum of thuis question - Can someone find the sum for this equation ...
For Further Reading
