solve : 3^x+3 = 9^x-2

Question

its a logarithm equation

Answer 1

Hello Jenny...

are (x+3) and (x-2) together as a power or is it (3^x)+3 and (9^x)-2

 

D. Y. Taylor

Answer 2

Hi Jenny,

 

I will make an assumption here that (x+3) is the exponent for 3 and (x-2) is the exponent for 9

 

3^x+3 = 9^x-2

 

get a common base

 

3^{x+3 =} 3^2(x-2)

 

Since the base is equal we can the exponents must be equal

 

x+3 = 2(x-2)

 

x+3 = 2x-4

 

x = 7

 

Hope this helps