Exponents of Real Numbers

Number Theory Level 1

If 1 0 x = 64 10^{x}=64 , then what is the value of 1 0 x 2 + 1 \large 10^{\frac{x}{2}+1} ?

80 18 42 81

Yash Chaudhary by yash chaudhary , 16, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Chew-Seong Cheong
Oct 31, 2018

1 0 x 2 + 1 = 10 ⋅ 1 0 x 2 = 10 1 0 x = 10 64 = 10 ⋅ 8 = 80 10^{\frac x2 + 1} = 10\cdot 10^\frac x2 = 10 \sqrt{\color{#3D99F6}10^x} = 10 \sqrt{\color{#3D99F6}64} = 10 \cdot 8 = \boxed{80} .

0 Helpful 0 Interesting 1 Brilliant 0 Confused
X X
Oct 28, 2018

1 0 0.5 x + 1 = 1 0 0.5 x × 10 = ( 1 0 x ) 0.5 × 10 = 6 4 0.5 × 10 = 80 10^{0.5x+1}=10^{0.5x}\times10=(10^x)^{0.5}\times10=64^{0.5}\times10=80

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...