I can simply do the problem by guess checking but because it is taking far too long, what is the simplest way to do these problems? Examples

27^4x = 9^x+1

Thanks~

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- Jul 22nd 2007, 09:25 AMJonathanEyoonExponential equation
I can simply do the problem by guess checking but because it is taking far too long, what is the simplest way to do these problems? Examples

27^4x = 9^x+1

Thanks~ - Jul 22nd 2007, 09:29 AMJhevon
get both bases in terms of the same base.

i assume you mean, $\displaystyle 27^{4x} = 9^{x + 1}$ ?....use parentheses! you should have typed 27^(4x) = 9^(x + 1) if that is the case

note that $\displaystyle 27 = 3^3$ and $\displaystyle 9 = 3^2$

so we have:

$\displaystyle \left( 3^3 \right)^{4x} = \left(3^2 \right)^{x + 1}$

$\displaystyle \Rightarrow 3^{12x} = 3^{2x + 2}$

can you take it from here? - Jul 22nd 2007, 09:33 AMJonathanEyoon