Solve the following exponential equations without using logs

Solve the following exponential equations without using logs: 2^2x+1 = 2^7 4^x - 2 = 8^3x 0.25^x = 16^x+6 (1/100)^x+1 = 10^x-1 Solve the following logarithmic equations: ln (4x + 5) - ln x = ln 5 2 ln (x - 5) = ln (x + 7) + ln 6 log_5 (6x - 2) = 4 log x - log (x + 2) = -1

Solution

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1)
	2^(2x+1)	=	2^(7)
=>	2x+1	=	7
	2x	=	6
	x	=	3
2)
	4^(x-2)	=	8^(3x)
	2^(2x-4)	=	2^(9x)
	2x-4	=	9x
	7x	=	-4
	x	=	-4/7
3)
	0.25^(x)	=	16^(x+2)
	0.25^(x)	=	(0.25)^(-2)(x+2)
	x	=	-2x-4
	3x	=	-4
	x	=	=4/3
4)
	(1/100)^(x+1)	=	10^(x-1)
	10^(-2x)	=	10^(x-1)
	-2x	=	x-1
	3x	=	1
	x	=	1/3