Question

1)1/(lg(x)+3)+2/(3-lg(x))=1

2)(log3x)^2-1/2*log3x^2=2

1/(lg(x)+3)+2/(3-lg(x))=1

7^x-2^(x+2)=5*7^(x-1)-2^(x-1)

x^(log3(x-4))=1/27

logx(9x^2)*(log3x)^2=4

Answer 1

$7^{x}-2^{x+2}=5*7^{x-1}-2^{x-1}$
$7^{x}-4*2^{x}=5* frac{1}{7}* 7^{x}- frac{1}{2}* 2^{x}$
$7^{x}-frac{5}{7}* 7^{x}=4*2^{x}- frac{1}{2}* 2^{x}$
$7^{x}(1-frac{5}{7})=2^{x}(4- frac{1}{2})$
$7^{x}*frac{2}{7}=2^{x}* frac{7}{2}$
$frac{7^{x}}{2^{x}}= frac{49}{4}$
$(frac{7}{2})^{x} = (frac{7}{2})^{2}$
x=2