((81^x-2)/(27^x))=9Im getting a bit confused with this one, thanks for your help :)
1 answer:
81, 27 and 9 are all powers of 3.
Let's write them in terms of 3.
81 = 3^4
Therefore we can write,
and since 27 = 3^3 we can write,
and 9 is 3^2.
So our equation looks like this,
Applying our exponent rule, division to subtraction, gives us,
And from this point, since the BASES are the same,
we can simply equate the exponents:
4(x-2)-3x = 2
and then solve for x.
Let's write them in terms of 3.
81 = 3^4
Therefore we can write,
and since 27 = 3^3 we can write,
and 9 is 3^2.
So our equation looks like this,
Applying our exponent rule, division to subtraction, gives us,
And from this point, since the BASES are the same,
we can simply equate the exponents:
4(x-2)-3x = 2
and then solve for x.
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The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9
<h3>How to determine the quadratic equation?</h3>From the question, the given parameters are:
Roots = (-1 - √2)/3 and (-1 + √2)/3
The quadratic equation is then calculated as
f(x) = The products of (x - roots)
Substitute the known values in the above equation
So, we have the following equation
This gives
Evaluate the products
Evaluate the like terms
So, we have
f(x) = x²+ 2/3x - 1/9
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