Video: Simplifying Equations Using Laws of Logarithms

Evaluate π‘š = 9𝑒^(ln 7) .

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Video Transcript

Evaluate π‘š equals nine multiplied by 𝑒 to the power of ln seven.

So if we take a look at what we’ve got, we’ve got π‘š equals nine multiplied by 𝑒 to the power of ln seven. Well, to solve this, we can use an identity we know. And our identity is that 𝑒 to the power of ln π‘₯ is equal to π‘₯. So therefore, we can say that 𝑒 raised to the natural logarithm of π‘₯ will just give us the result of π‘₯. And if we apply this to ours, what we’re gonna have is nine multiplied by seven. And that’s because seven was our π‘₯ because it was ln seven or the natural algorithm of seven.

So therefore, we can say that π‘š is equal to 63.

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