Question

6) Resolva a equação exponencial : ( 0,0001 )3x+4 = 100000000

Answer 1

Explicação passo-a-passo:

$(0.0001)^{3x + 4} = 100000000 \\ ({ \frac{1}{10000} })^{3x + 4} = {10}^{8} \\ ( { \frac{1}{ {10}^{4} } )}^{3x + 4} = 10^{8} \\ (\frac{1^{4} }{10^{4} } )^{3x + 4} = 10^{8} \\( ( \frac{1}{10} )^{4} )^{3x + 4} = 10^{8} \\ ( \frac{1}{10} )^{4(3x + 4)} = 10^{8} \\ { \frac{1}{10} }^{12x + 16} = {10}^{8} \\( {10}^{ - 1} )^{12x + 16} = {10}^{8} \\ {10}^{ - 1(12x + 16)} = {10}^{8} \\ {10}^{ - 12x - 16} = {10}^{8} \\ - 12x - 16 = 8 \\ - 24 = 12x \\ x = \frac{ - 24}{12} = - 2 \\ x = - 2$