What is the true solution to 3 ln 2+ln 8=2ln(4x)
2 answers:
Answer:
x = 2
Step-by-step explanation:
Using the rules of logarithms
• log ⇔ nlog x
• log x + log y ⇔ log(xy)
• log x = log y ⇒ x = y
Given
3 ln2 + ln8 = 2ln(4x)
ln2³ + ln8 = ln(4x)²
ln8 + ln8 = ln16x²
ln(8 × 8) = ln16x²
ln64 = ln16x², hence
16x² = 64 ( divide both sides by 16 )
x² = 4 ( take the square root of both sides )
x = = 2
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Given:
The sequence is:
-15,-10,-4, 3, 11, ______
To find:
The next number.
Solution:
We have,
-15,-10,-4, 3, 11, ______
Here, the difference between two consecutive terms are:
Similarly,
It is clear that the difference difference between two consecutive terms is increasing by 1. So, the next difference must be (8+1)=9.
Let the next number be x. Then,
Therefore, the next number of the sequence is 20.
Case 1: The length of the third side (hypotenuse) is <u>5</u>m.
My Reasoning/Work:
We use the Pythagorean theorem (a^2+b^2=c^2), the two legs in the Pythagorean theorem are "a" and "b" and the third leg/the hypotenuse, is "c".
Then, we find the squares of 3 and 4, and then add them up.
Now that we know that the square of the third side is 25m, we now find the square root of 25.
The hypotenuse is 5m.
Case 2: The length of the third side (the leg) is <u>
</u>m.
My Reasoning/Work:
Again, we'll use the Pythagorean theorem.
This time, instead of using the "b", we're using the "a" (leg) and the "c" (hypotenuse). Because the hypotenuse is the longest side in a right triangle, we get that "c" is equal to 4m.
And now we bring down the exponents.
We now subtract 9 from both sides to leave the "b^2" alone.
Finally, we find the square root of 7 to get the answer. But if you use a calculator to find this, you'll get an annoying answer of decimals (2.645751311064591). So, to simplify this, the answer would be
.<u />
My Reasoning/Work:
We use the Pythagorean theorem (a^2+b^2=c^2), the two legs in the Pythagorean theorem are "a" and "b" and the third leg/the hypotenuse, is "c".
Then, we find the squares of 3 and 4, and then add them up.
Now that we know that the square of the third side is 25m, we now find the square root of 25.
The hypotenuse is 5m.
Case 2: The length of the third side (the leg) is <u>
My Reasoning/Work:
Again, we'll use the Pythagorean theorem.
This time, instead of using the "b", we're using the "a" (leg) and the "c" (hypotenuse). Because the hypotenuse is the longest side in a right triangle, we get that "c" is equal to 4m.
And now we bring down the exponents.
We now subtract 9 from both sides to leave the "b^2" alone.
Finally, we find the square root of 7 to get the answer. But if you use a calculator to find this, you'll get an annoying answer of decimals (2.645751311064591). So, to simplify this, the answer would be