The way you did it is correct. if a = -4, the 3(-4)+4 = -8, so we have \(3^{-8}\) and \(9^{-4}\) These both are equal to:
\(\frac{1}{3^8}\) and \(\frac{1}{9^4}\); \(9^4 = (3^2)^4 = 3^8\)
SIDE NOTE:
When dealing with exponents, if you change the base, you obviously have to change the power as well. If you go from \(9^4\) you represent that first as \((3^2)^4\) and then multiply the exponents. So you have \(3^8\) What if you wanted to turn \(3^8\) into a base of 27? \(3^8 = 27^x\), what is x? Take whatever power you used to change the base, such as here, 3 to 27 is a 3 to a power of 3, or \(3^3\), then the existing exponent is divided by the power used to alter the base.
\(3^8 = 27^x\)
\((3^z)^{\frac{8}{z}} = (3^z)^x\) so x = \(\frac{8}{z}\)
In this situation: \(3^8 = 27^x\) x = \(\frac{8}{3}\)
to solve this, we would really need to turn 4 into a power of 3. This power is going to be some fraction such as \(\frac{x}{z}\)
\(\sqrt[z]{3^x}\)
and then to get rid of the root, we'd have to take each other element by a power of z and it would create a horrible mess. I think your answer has to be right at -4 and the OA is wrong. What is the source of this question?
The only way I think it could be different is if the question actually meant \(3^{3a}+4=3^{2a}\)
darlameow wrote:
Question, What is the value of (a) if 3^3a+4=9^a
3^3a+4=3^2a
3a+4=2a
a=-4
but the answer key says the answer should be 4
Any suggestions! Thanks........