1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that
, so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:


Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Answer: -5/12
Step-by-step explanation: Before multiplying two fractions together by multiplying across their numerators and multiplying across their denominators, you should always try to cross-cancel as your first step.
So in this problem, the 2 and 8 cross-cancel to 1 and 4.
Also, watch out for your signs. In this problem we have a negative times a positive so we know that our answer will be negative.
Now we can multiply across the numerators and across the denominators.
So we have 5 · 1 which is 5 and 4 · 3 which is 12.
So our answer is -5/12.
Be very careful with your signs!
Answer: yes, just tell me the problem
Step-by-step explanation:
Answer:
EB=3.3
Step-by-step explanation:
From the diagram, triangle ABC is similar to triangle DBE.
This means that, the corresponding sides are proportional.
It was given that AC=6, DE=4, CB=5.
We want to find EB=x
Since the ratio of corresponding sides are proportional, we have:

We substitute to obtain:
Multiply both sides by 5 to get:
