WEBVTT
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Find to the nearest hundredth the value of π₯ for which two to the power of π₯ plus eight equals nine.
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Now the first stage to actually solve this equation is take logs of both sides and this gives us log of two to the power of π₯ plus eight equals log of nine.
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And what we say here by log is log to the base 10.
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So if we donβt write a base, it automatically means log to the base 10.
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So if you actually press log in your calculator, then itβs actually gonna calculate as if itβs log to the base 10.
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Okay, great, but what do we do now?
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Well, weβre actually gonna use a log law to help us solve the equation.
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And the one weβre gonna use is that log π΄ to the power of π is equal to π log π΄.
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And by applying this law, we get π₯ plus eight log two equals log nine.
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And we get this because π₯ plus eight was our π and two was our π΄.
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Okay, great, so now whatβs the next step?
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Well, the next step is to actually divide each side by log two, which gives us π₯ plus eight is equal to log nine over log two.
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So then, we actually subtract eight from each side.
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So therefore, we can say that π₯ is equal to log nine over log two minus eight, which if we put into calculator, we get π₯ is equal to negative 4.8300749986.
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So then, we take a look back at the question to see how it wants us to actually leave our answer.
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And the question says that it wants us to leave it to the nearest hundredth.
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So therefore, we know that π₯ is equal to negative 4.83.