Question

Given that 2^(2x+3) x 7^x-2 = 2^3x (49^x), evaluate 14^x

Answer 1

start wid dividing the whole equation wid \(2^{2x+3} 7^{x-2}\)

Answer 2

done it

Answer 3

\(\large 2^{2x+3} 7^{x-2} = 2^{3x} (49^x)\)

\(\large 1 = \frac{2^{3x} (49^x)}{2^{2x+3} 7^{x-2}}\)

Answer 4

use exponent properties, and get rid of denominator in right hand side

Answer 5

also see that you can write 49 as 7^2

Answer 6

seen it i'm ready to move on

Answer 7

\(\large 2^{2x+3} 7^{x-2} = 2^{3x} (49^x)\)

\(\large 1 = \frac{2^{3x} (49^x)}{2^{2x+3} 7^{x-2}}\)

\(\large 1 = \frac{2^{3x} (7^{2x})}{2^{2x+3} 7^{x-2}}\)

\(\large 1 = \frac{2^{x} (7^{x}) 7^2}{2^{3} }\)

\(\large 1 = \frac{14^{x} 7^2}{2^{3} }\)

Answer 8

Thanks for teaching me...

Answer 9

np :)