Question

If 49^a=343^b,then a:b is

Answer 1

Hi there❤️

_______________________

$49 {}^{a} = 343 {}^{b} \\ \\ (7 {}^{2} ){}^{a} = (7 {}^{3}) {}^{b} \\ \\ \cancel{7} \: {}^{2a} = \cancel7 \: {}^{3b} \\ \\ 2a = 3b$

Therefore,

a : b = 2 : 3

_______________________

Thanks !

@AarohiG ❤️

Answer 2

${49}^{a} = {343}^{b} \\ \\ we \: know \: \\ \\ factors \: of \: 49 = 7 \times 7 \\ \\ factors \: of \: 343 = 7\times 7 \times 7 \\ \\ thus \: it \: can \: also \: be \: written \: as \\ \\ {7}^{2a} = {7}^{3b} \\ \\ 2a = 3b \\ \\ thus \: \frac{a}{b} = \frac{3}{2} \\ \\ hope \: this \: helps \: you$
(^^)✌