Determine which number is a solution of the equation. q divide 8 = 56
1 answer:
Answer: q = 56
Step-by-step explanation: First rewrite the problem to be
In this problem, notice that <em>q</em> is being divided by 8 so to get <em>q</em> by itself, we need to multiply both sides of the equation by 8.
Notice that on the left side the 8 and 8 cancel each other out so we're just left with <em>q</em>. On the right side, we have
56 x 8 which is 448 so <em>q = 448</em>.
Finally, we can check our answer by plugging a 488 back into the original equation. So we have which is a true statement so our answer checks.
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This equation uses two properties of logarithms:
So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15
So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15