Respuesta :

Louli
Answer:
x = 50

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

[tex] \frac{2x}{2} [/tex] = [tex] \frac{10^2}{2} [/tex]

x = 50

Hope this helps :)

Answer:

For [tex]2log2x=4[/tex] , x = 50

Step-by-step explanation:

Given : [tex]2log2x=4[/tex]

We have to find the value of x.

Consider the given [tex]2log2x=4[/tex]

Divide both side by 2, we have,

[tex]\frac{2\log _{10}\left(2x\right)}{2}=\frac{4}{2}[/tex]

Simplify, we have,

[tex]\log _{10}\left(2x\right)=2[/tex]

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

[tex]2=\log _{10}\left(10^2\right)=\log _{10}\left(100\right)[/tex]

[tex]\log _{10}\left(2x\right)=\log _{10}\left(100\right)[/tex]

When log have same base, we have,

[tex]\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)[/tex]

We have,

[tex]2x=100[/tex]

Divide both side by 2, we have,

[tex]x=50[/tex]

Thus, For [tex]2log2x=4[/tex] , x = 50

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