SOLUTION: solve for x: 1) 8^5X = 4 2)125^2x+9 =1/5 please help me with these 2 problems I have for math. I am struggling to get by. Thankyou for your time and effort.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for x: 1) 8^5X = 4 2)125^2x+9 =1/5 please help me with these 2 problems I have for math. I am struggling to get by. Thankyou for your time and effort.      Log On


   

Question 598857: solve for x:
1) 8^5X = 4
2)125^2x+9 =1/5


please help me with these 2 problems I have for math. I am struggling to get by.
Thankyou for your time and effort.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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Solve for x:
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8%5E%285x%29=4
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One way to solve this problem is to rewrite both sides of the equation in terms of the same base. Then use the exponent laws to simplify and solve for x.
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8 = 2^3 and 4 = 2^2, so let's re-write the equation in base 2.
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%282%5E3%29%5E%285x%29=2%5E2
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When you raise an exponential expression to a power, multiply the exponents. Since the both sides of the equation are equal, and both sides are raising 2 to a power, the powers must be the same. Therefore,
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#1
3%2A5x=2
15x=2
x=2%2F15
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Check your solution using the original equation.
8%5E%285x%29=4
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8%5E%285%2A%282%2F15%29%29=4
8%5E%282%2F3%29=4
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8^(2/3) is the third root of 8^2. 8^2 is 64. Notice that 64 = 4*4*4. The third root of 4*4*4 is 4. So our solution works.
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#2
125%5E%282x%2B9%29=1%2F5
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We'll use a similar process here. This time re-write both sides of the equation in terms of base 5. [125=5*5*5=5^3 and 1/5 = 5^(-1)].
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5%5E%283%2A%282x%2B9%29%29=5%5E%28-1%29
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Set the exponents equal to each other.
3%2A%282x%2B9%29=-1
6x%2B27=-1
6x=-28
x=-28%2F6
x=-14%2F3
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Check your work using the original equation.
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125%5E%282x%2B9%29=1%2F5
125%5E%282%28-14%2F3%29%2B9%29=1%2F5
125%5E%28-28%2F3%2B9%29=1%2F5
125%5E%28-28%2F3%2B27%2F3%29=1%2F5
125%5E%28-1%2F3%29=1%2F5
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125^(-1/3) means 1 divided by the third root of 125. The third root of 125 is 5, and 1 divided by 5 is 1/5. Check!
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Hope this helps. Email if you have questions.
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Ms.Figgy
math.in.the.vortex@gmail.com