Question

log(2) {2+3.log(3) [1+4.log(4) (5x+1) ] } = 3

Answer 1

$\log_{2} \{2+3.\log_{3} [1+4.\log_{4} (5x+1) ] \} = 3$

$2+3.\log_{3} [1+4.\log_{4} (5x+1) ] = 2^{3}$

$2+3.\log_{3} [1+4.\log_{4} (5x+1) ] = 8$

$3.\log_{3} [1+4.\log_{4} (5x+1) ] = 8-2$

$3.\log_{3} [1+4.\log_{4} (5x+1) ] = 6$

$\log_{3} [1+4.\log_{4} (5x+1) ] = \dfrac{6}{3}$

$\log_{3} [1+4.\log_{4} (5x+1) ] = 2$

$1+4.\log_{4} (5x+1) = 3^{2}$

$1+4.\log_{4} (5x+1) = 9$

$4.\log_{4} (5x+1) = 9-1$

$4.\log_{4} (5x+1) = 8$

$\log_{4} (5x+1) = \dfrac{8}{4}$

$\log_{4} (5x+1) = 2$

$5x+1= 4^{2}$

$5x+1= 16$

$5x= 16-1$

$5x= 15$

$x =\dfrac{15}{5}$

$x =3$

$S=\{3\}$