SOLUTION: Step-by-step solution of: {{{ 5^(2x+1) = 25^x*5^(3*x) }}}

SOLUTION: Step-by-step solution of: {{{ 5^(2x+1) = 25^x5^(3x) }}}

Question 1087279: Step-by-step solution of:

Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

........if base same, exponents are same too

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
5^(2x+1) = 25^(x) * 5^(3x)
:
Note 25^(x) * 5^(3x) = (5^2)^(x) * 5^(3x) = 5^(2x) * 5^(3x) = 5^(5x)
:
5^(2x+1) = 5^(5x)
:
take logarithms of both sides of =
:
log(5) (2x+1) = 5log(5) (x)
:
divide both sides of = by log(5)
:
2x + 1 = 5x
:
3x = 1
:
*******
x = 1/3
*******
:

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