Answer: x = log₃₇(12)
Step - by - step explanation:
1. Remove the variable from the exponent using logarithms
37^x=12
Take the common logarithm of both sides of the equation:
log₁₀(37^x)=log₁₀12)
Use the log rule: log_a(x^y)=y*log_a(x) to move the exponent outside the logarithm:
x*log₁₀(37)=log₁₀(12)
2. Isolate the x-variable
x*log₁₀(37)=log₁₀(12)
Divide both sides of the equation log₁₀(37) by:
x = log₁₀(12) / log₁₀(37)
Use the formula ![log_{b}(x)/log_{b}(a) = log_{a} (x)](https://tex.z-dn.net/?f=log_%7Bb%7D%28x%29%2Flog_%7Bb%7D%28a%29%20%3D%20log_%7Ba%7D%20%28x%29)
to combine the logarithms into one:
x=log₃₇(12)
Decimal form:
x=0.6881648129099501
Hope this helps!
0.25x² + 8.5 - 17 = 0
1)
a = 0.25
b = 8.5
c = -17
2)
- 8.5 ± √(8.5)²-4(0.25) (-17)
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2(0.25)
3)
-34 ± √1428
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2
4)
-35.894 and 35.894
Answer:
Step-by-step explanation:
Perpendicular lines are lines whose slopes are the negative reciprocal of each other.
So, in this case, the other line's slope is ![-10](https://tex.z-dn.net/?f=-10)
Now we can use
![y = mx + b\\y = -10x + b\\9 = -10(3) + b\\9 = -30 + b\\b = 39\\y = -10x + 39](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b%5C%5Cy%20%3D%20-10x%20%2B%20b%5C%5C9%20%3D%20-10%283%29%20%2B%20b%5C%5C9%20%3D%20-30%20%2B%20b%5C%5Cb%20%3D%2039%5C%5Cy%20%3D%20-10x%20%2B%2039)
The problem here takes a brilliant mind to answer this. This problem can easily be answered using programming because we can not then and there push all the possibilities using paper and pen.
The answer is <span>3816547290.
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Trying all the possibilities starting form 1000000080 (we are sure that the last number should be 0). Then traversing that number until <span>9999999990. Each traverse, check the number if its divisible to n, so on and so forth.
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