Question

Condense:

Ln 40 + 2 ln 1/2 + ln x

Answer 1

ln(40) + 2ln(1/2) + ln(x)

First, you should take the 2 and put it back in the argument. Since it's a coefficient, when you put it back it in would be a power. That changes 2ln(1/2) to ln(1/2 ^ 2), which is ln(1/4).

ln(40) + ln(1/4) + ln(x)

Then, to add these, we just multiply the arguments, meaning we just have:

ln(40 * 1/4 * x)

Multiply and then we're done.

ln(10x)

Answer 2

Using logarithmic function, the condense of Ln 40 + 2 ln 1/2 + ln x is ln(10x).

What is logarithmic function?

Logarithmic function is function is an " inverse of an exponential function so that the independent variable appears logarithmic function".

According to question,

Ln 40 + 2 ln 1/2 + ln x

Properties of Logarithmic function     $x ln (a) = ln(a^x)$.

Using above properties we can write $2 ln \frac{1}{2}$ $= ln(a^(\frac{1}{2})^2)$ $=ln(a^\frac{1}{4})$.

Properties of Logarithmic function $ln(a) + ln(b) = ln(ab)$

Using above properties we can write Ln 40 + 2 ln 1/2 + ln x as $ln(40 . \frac{1}{4}.x)$.

= $ln(10x)$

Hence, Using logarithmic function, the condense of Ln 40 + 2 ln 1/2 + ln x is ln(10x).

Learn more about Logarithmic function here

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