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4 years ago

5

Plz help me I’ll give branliest!!

1 answer:

padilas [110]4 years ago

5 0

Answer:

I is the 3rd answer

Step-by-step explanation:

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

zepelin [54]

Answer:

<em>x = 2</em>

Step-by-step explanation:

<u>Exponential Equations</u>

Solve:

$5^{2x-1}+5^{x+1}=250$

Separate each exponential:

$5^{2x}5^{-1}+5^{x}5^{1}=250$

Operating:

$\displaystyle \frac{5^{2x}}{5}+5^{x}5=250$

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

8 0

3 years ago