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1 vote
Solve 2 log 2x = 4. Round to the nearest thousandth if necessary

2 Answers

2 votes

Answer:

For
2log2x=4 , x = 50

Step-by-step explanation:

Given :
2log2x=4

We have to find the value of x.

Consider the given
2log2x=4

Divide both side by 2, we have,


(2\log _(10)\left(2x\right))/(2)=(4)/(2)

Simplify, we have,


\log _(10)\left(2x\right)=2


\mathrm{Apply\:log\:rule}:\quad \:a=\log _b\left(b^a\right)


2=\log _(10)\left(10^2\right)=\log _(10)\left(100\right)


\log _(10)\left(2x\right)=\log _(10)\left(100\right)

When log have same base, we have,


\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)

We have,


2x=100

Divide both side by 2, we have,


x=50

Thus, For
2log2x=4 , x = 50

User Mischa Kroon
by
8.2k points
1 vote
Answer:
x = 50

Step-by-step explanation:
Before we begin, remember the following:
logₐ (x) = b
is equivalent to:
a
= x

log with no base written has the default base 10

Now, let's check the given:
2 log 2x = 4

We will start by dividing both sides by 2:
log 2x = 2

Now, applying the above rules, we can get the value of the x as follows:
log 2x = 2
10
² = 2x


(2x)/(2) =
(10^2)/(2)

x = 50

Hope this helps :)
User Clare Barrington
by
7.6k points

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