Question

2x-lg(5^2x+4x-16)=lg4^x

Answer 1

$2x-lg(5^{2x}+4x-16)=lg4^x\\ 2xlg10-lg(5^{2x}+4x-16)=lg4^x\\ lg10^{2x}-lg(5^{2x}+4x-16)=lg4^x\\ lg10^{2x}-lg4^x=lg(5^{2x}+4x-16)\\ lg \frac{10^{2x}}{4^x} =lg(5^{2x}+4x-16)\\ ( \frac{10^2}{4})^x= 5^{2x}+4x-16\\ 25^x= 5^{2x}+4x-16\\ 5^{2x}- 5^{2x}=4x-16\\ 4x-16=0\\ 4x=16\\ x=4$
Проверка:
$2\cdot4-lg(5^{2\cdot4}+4\cdot4-16)=lg4^4\\ 8-lg5^{8}=lg4^4\\ 8=lg4^4+lg5^{8}\\ 8=lg(4^4\cdot5^{8})\\ 8=lg(2^8\cdot5^{8})\\ 8=lg10^8\\ 8=8$