Question

Exercício 2) Dados o log 2= 0,3 e log 3~0,48
encontre o valor de x na equação 18
x=20.​

Answer 1

Explicação passo-a-passo:

$\sf 18^x=20$

$\sf log~18^x=log~20$

$\sf x\cdot log~18=log~20$

$\sf x\cdot log~(2\cdot3^2)=log~(2^2\cdot5)$

$\sf x\cdot(log~2+log~3^2)=log~2^2+log~5$

$\sf x\cdot(log~2+2\cdot log~3)=2\cdot log~2+log~\Big(\dfrac{10}{2}\Big)$

$\sf x\cdot(log~2+2\cdot log~3)=2\cdot log~2+log~10-log~2$

$\sf x\cdot(0,3+2\cdot0,48)=2\cdot0,3+1-0,3$

$\sf x\cdot(0,3+0,96)=0,6+1-0,3$

$\sf x\cdot1,26=1,3$

$\sf x=\dfrac{1,3}{1,26}$

$\sf x=\dfrac{130}{126}$

$\sf x=\dfrac{65}{63}$

$\sf \red{x\approx1,032}$