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Professor Dave here, lets solve some equations. Now that we know what logarithms are, we are ready to solve exponential and logarithmic equations. Take something like two to the X equals sixteen. Its true that we could just intuitively understand that X must be four, because we can see that two must be raised to the fourth power for this equation to be valid. But things get trickier when this number isnt so obvious. What about two to the X equals seventeen? If youre not a computer, you cant do this in your head, so we have to use logarithms. Taking the log base two of both sides gives us this. Now it follows that two to this power equals two to the X power, so X must be equal to log base two of seventeen. This may not be aesthetically pleasing, but it is the precise solution for this equation. If we wanted to get an answer that can be plugged into a calculator, we could instead take two to the X equals seventeen and just take the natural log of both sides. Then, we could drag this
