Answer:
x = 1/2
Step-by-step explanation:
1) Using logarithms
5^(2x +1) = 25
log₅(5^(2x +1)) = log₅(25) . . . . take log base 5
2x +1 = 2 . . . . . . . . . . . . . . . . simplify
2x = 1 . . . . . . . . . . . . . . . . . subtract 1
x = 1/2 . . . . . . . . . . . . divide by 2
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2) Equating exponents (basically, the same thing)
5^(2x +1) = 25
(5^(2x))(5^1) = 25
5^(2x) = 25/5 = 5^1
2x = 1 . . . . . equate exponents
x = 1/2
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3) See attached for a graphical solution to ...
f(x) = 5^(2x+1) -25
for f(x) = 0
The x-intercept is shown as x = 0.5.
