Question

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

Answer 1

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

Answer 2

Answer:
x = 50

Step-by-step explanation:
Before we begin, remember the following:
logₐ (x) = b
is equivalent to:
aᵇ = 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
10² = 2x


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

x = 50

Hope this helps :)