Three Exponential Equations

Question

Could any of you guys assist me with the following questions. Thanks. I first tried moving everything to one side, but don't know how to continue.

Solve the following algebraically:

Question 1: $$5^{2x+1} + 25 = 5^{x+3} + 5^x$$

Answer is:

$x= -1 ,2$

Question 2: $$8^x +7\times2^{x+1} = 7\times4^x+8$$

Answer is:

$x= 0,1 , 2$

Question 3: $$3^{3x} -12\times9^x + 63\times 3^x = 4\times3^3$$

Answer is:

$x=1$

Thanks in advance.

Answer 1

HINT: write your first equation as $$5\cdot (5^x)^2+25=125\cdot 5^x+5^x$$ and your second equation as $$(3^x)^3+14\cdot 2^x=7\cdot (2^x)^2+8$$ and the last one as $$(3^x)^3-12\cdot (3^x)^2+63\cdot 3^x=4\cdot 3^3$$

Answer 2

Hint:

all these can be solved by substitution. In the first use $y=5^x$, in the second $y=2^x$ and do yourself for the last one.