You can put this solution on YOUR website! All logarithms are to the base 8 in this problem.
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when two logs are subtracted, it is equivalent to the log of their quotient in which the
negative log becomes the denominator. By this rule the problem can be converted to:
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Now you can convert this to exponential form by raising the base (8) to the exponent
on the right side of the equation (1) and setting that equal to the term on which the log
function is operating . In equation form this is:
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This simplifies to:
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Get rid of the denominator on the right side by multiplying both sides by x to get:
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So the equation has been reduced to:
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Subtract x from both sides of this equation to get:
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Finally, divide both sides of the equation to get:
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That's the answer to the problem. Hope this helps you to understand a little bit more about
methods you can use to solve logarithmic equations. The conversion from logarithmic
form to exponential form is especially useful and you should become familiar with it.
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