Question

Resolva as equaçoes exponencial

a-) 10 elevado a x= √0,1 ??

B-) 2^4x-2/ 2^3x+2=1/2 ?

c-) 2^x-2=8/2^x-3?

Answer 1

a-)

${10}^{x} = \sqrt{ \frac{1}{10} } \\ {10}^{x} = {{(10}^{ - 1})}^{ \frac{1}{2} } \\ {10}^{x} = {10}^{ - \frac{1}{2} } \\ x = - \frac{1}{2}$

b-)

${2}^{4x - 2} \div {2}^{3x + 2} = 1 \div 2 \\ {2}^{4x - 2 - (3x + 2)} = {2}^{ - 1} \\ 4x - 2 - 3x - 2 = - 1 \\ x - 4 = - 1 \\ x = - 1 + 4 \\ x = 3$

c-)

${2}^{x - 2} = 8 \div {2}^{x - 3} \\ {2}^{x - 2} = {2}^{3} \div {2}^{x - 3} \\ {2}^{x - 2} = {2}^{3 - (x - 3)} \\ x - 2 = 3 - x + 3 \\ 2x = 8 \\ x = 4$