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5^(2x-1)+5^(x+1)=250
how do you solve?
thank you

User IMUXIxD
by
6.9k points

1 Answer

3 votes

Answer:

x = 2

Explanation:

Exponential Equations

Solve:


5^(2x-1)+5^(x+1)=250

Separate each exponential:


5^(2x)5^(-1)+5^(x)5^(1)=250

Operating:


\displaystyle (5^(2x))/(5)+5^(x)5=250

Multiplying by 5:


5^(2x)+25\cdot5^x=1250

Rearranging:


5^(2x)+25\cdot5^x-1250=0

Recall that:


5^(2x)=(5^(x))^2


(5^(x))^2+25\cdot5^x-1250=0

Calling


y=5^(x):


y^2+25y-1250=0

Factoring:


(y-25)(y+50)=0

There are two possible solutions:

y=25

y=-50

Since


y=5^(x)

y cannot be negative, thus:


5^(x)=25=5^2

The solution is:

x = 2

User Peter Hawkins
by
6.8k points