1. ## Log question

Im pretty sure im meant to be solving this as a logarithim.
Question is:

Find all real solutions if any of:

3^x multiply 27^(2-x) = 9

Very confused...

Thanks.

PS pleaqse include working so i can study it when youre done.

2. ## Re: Log question

Originally Posted by Hooperoo
Im pretty sure im meant to be solving this as a logarithim.
Question is:

Find all real solutions if any of:

3^x multiply 27^(2-x) = 9

Very confused...

Thanks.

PS pleaqse include working so i can study it when youre done.
$\displaystyle 3^x \cdot 27^{2-x}=9$

$\displaystyle 3^x \cdot 3^{6-3x}=3^2$

$\displaystyle 3^{6-2x}=3^2$

$\displaystyle 6-2x=2$

$\displaystyle x=2$

3. ## Re: Log question

I use to love problems like this because it would be like one of those hidden things... The first thing that would come into my mind is how are all these numbers kinda related so 3, 9 and 27. All multiples of 3 right... and if we are dealing with exponents then you kind of got to say, "Ok, well... 9 = 3 to the what (3^?)... oh (3^2) = 9" and so on.

Just a quick tip if anyone else is reading