Question

if log 2=a, log 3= b, log 7= c and
${2}^{ x}. {3}^{x + 4} = {7}^{x}$
Then the value of x in terms of a, b, c is​

Answer 1

Good Night

$log_{}(2) = a \: \: \: log(3) = b \: \: log(7) = c \: \: \\ \\ 2 {}^{x} \times 3 {}^{x + 4} = 7 {}^{x} \\ taking \: log \: on \: both \: sides \: we \: have \\ \\ log(2 {}^{x} \times 3 {}^{x + 4} ) = log(7 {}^{x} ) \\ \\ log(2 {}^{x} ) + log(3 {}^{(x + 4)} ) = log(7 {}^{x} ) \\ becoz \: \: log(mn) = log(m) + log(n) \\ \\ x log(2) + (x + 4) log(3) = x log(7) \\ becoz \: \: log(y {}^{n} ) = n log(y) \\ \\ x \times a + ( x+ 4) \times b = x \times c \\ \\ ax + bx - cx = - 4b \\ \\ x = \: \: \: \: \: - 4b \\ \: \: \: \: \: \: \: \: - - - - - - \\ \: \: \: \: \: \: \: \: \:a + b - c$