Please help Meh
Which of the following options is an equivalent function to f(x) = 3(2)^3^x?
(both 3 and x are listed as exponents :)

Question

Please help Meh
Which of the following options is an equivalent function to f(x) = 3(2)^3^x? 
(both 3 and x are listed as exponents :)

anonymous · Answer

please help @phi

phi · Answer

is it 
$$  f(x) = 3(2)^{3^x} $$?

phi · Answer

or
$$ f(x)= 3(2)^{3x} $$
?

phi · Answer

we can't do much with the first.  the second can be written as
$$ f(x)= 3(2^3)^x = 3\cdot 8^x$$

anonymous · Answer

whats the difference between the two equations? @phi sorry my mum called me

phi · Answer

the first one has  $3^x$ as the exponent. the second way has 3x  as the exponent.
the first way can't be simplified.
the second way can be, using the rule
$$ a^{bc}= (a^b)^c $$

anonymous · Answer

(3x) is an exponent, they are both together and  the same location/size... @phi

phi · Answer

that means you can write the 2^(3x)  as either
$$ (2^x)^3 $$
or
$$ (2^3)^x$$
the second way means
$$ (2\cdot 2\cdot 2)^x
$$
or $$8^x$$

phi · Answer

and we still have a 3 out front so you could write the expression
3 * 2^(3x)  as
3*8^x

phi · Answer

Does that match any of your options?