Graph

Algebra Level 3

$\large g(x) = \log_{10} \left(2 \times \sqrt{25^{x^2}}\right) + \log_{10} \left(625 \times 2^{x^2+3}\right)$

Which of the options represents the graph of function $g(x)$ as defined above?

x^2+4

x^2+1

x^2-4

2x^2

1 solution

Zee Ell
Feb 4, 2017

$g(x) = \log _{10} (2 × \sqrt { 25^{ x^2 } } ) + \log _ {10} (625 × 2^{x^2 + 3} ) =$

$= \log _{10} (2 × 5^{ x^2 } ) + \log _ {10} (625 × 2^3 × 2^{x^2} ) =$

$= \log _{10} ( 2 × 5^{ x^2 } × 625 × 8 × 2^{x^2} ) = \log _{10} ( 10000 × 10^{ x^2 } ) =$

$= \log _{10} ( 10^{ x^2 + 4 } ) = \boxed { x^2 + 4 }$