Brain Easier

Algebra Level 2

If $49^x - 49^{x-1}=16464$ Then which of the following is equivalent of $(2x)^x$ ?

7^{7/2}

3^{3/2}

2^{2/2}

6^{8/2}

5^{5/2}

2 solutions

Chew-Seong Cheong
Apr 22, 2015

$49^{x}-49^{x-1}=16464 \quad \Rightarrow 49^{x-1}(49-1)=16464 \\ \Rightarrow 48(49^{x-1}) = 16464 \quad \Rightarrow 49^{x-1} = 343 \quad \Rightarrow 7^{2(x-1)} = 7^3 \\ \Rightarrow 2(x-1) = 3 \quad \Rightarrow x - 1 = \frac{3}{2} \quad \Rightarrow x = \frac{5}{2} \\ \quad \Rightarrow (2x)^x = \boxed{5^{\frac{5}{2}}}$

Nishant Kumar
Apr 22, 2015

49^x - 49^x-1=16464 ,,,,,

49^x(1-49^-1)=16464 ,,,,,

49^x(1-1/49)=16464 ,,,,,

49^x(48/49)=16464 ,,,,,

49^x/49=16464 /48 ,,,,,,

49^x-1=343 ,,,,,

7^2x-2=7^3 ,,,,,

2x-2=3 ; x=5/2 ,,,,,

so (2x)^x = (2*5/2)^5/2 ,,,,,

(5)^5/2

Nishant, you should learn up LaTex. You can mouse over any LaTex form in problems or solutions in Brilliant.org to see the keystrokes.

Chew-Seong Cheong - 6 years, 1 month ago

Brain Easier

2 solutions

0 pending reports