1. ## Exponential 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~

2. Originally Posted by JonathanEyoon
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~
get both bases in terms of the same base.

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

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

so we have:

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

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

can you take it from here?

3. Originally Posted by Jhevon
get both bases in terms of the same base.

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

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

so we have:

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

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

can you take it from here?

OHhhhhhhhhhh I totally forgot about base!! Thanks alot and I will use parentheses next time~