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mote1985 [20]
3 years ago
7

Solve: In 2x + In 2 = 0 DONE

Mathematics
1 answer:
pychu [463]3 years ago
7 0

Answer:

x=\frac{1}{4}

Step-by-step explanation:

We can use some logarithmic rules to solve this easily.

<em>Note: Ln means Log_e</em>

<em />

Now, lets start with the equation:

ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)

Writing left side with logarithmic base e, we have:

Log_{e}(2x) = -ln(2)

We can now use the property shown below to make this into exponential form:

Log_{a}b=x\\means\\a^x=b

So, we write:

Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x

We recognize another property of exponentials:

a^{bc}=(a^{b})^{c}

So, we write:

e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x

Also, another property of natural logarithms is:

e^{(ln(a))}=a

Now, we simplify:

(e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}

This is the answer.

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