What is the intersection point of the graphs of these two functions?

f(x)=1000*10^{x}

g(x)=8*2^{x}

I got up until f(x)= 10^{3x}

and g(x)= 2^{3x}

but I don't really know how to go further beyond that...

Guest Apr 22, 2023

edited by
Guest
Apr 22, 2023

#1**0 **

The graphs of the functions f(x)=1000∗10^x and g(x)=8∗2^x intersect when 1000∗10^x=8∗2^x. Dividing both sides by 2^x, we get 500∗10=4∗2^x. Dividing both sides by 4, we get 125∗5=2^x. Taking the logarithm of both sides, we get x=log2(125∗5). Evaluating this logarithm in base 2, we get x=4. Therefore, the intersection point of the graphs is (4,1024).

Guest Apr 22, 2023