You can put this solution on YOUR website! Solving an equation for a variable which is in a logarithm usually starts with using algebra and/or properties of logarithms to transform the equation into one of the following general forms:
log(expression) = number
or
log(expression) = log(other_expression)
To get
into the first form, all we need to do is divide both sides by -2.5:
Simplifying the left side we get:
The next step with the first form is to rewrite the equation in exponential form. In general is equivalent to . Using this pattern (and the fact that the base of "log" is 10) we get:
Now that the variables are out of the log we can solve. Since you posted "in terms of x" I'm assuming that we are supposed to solve for y in terms of x. For this we just multiply both sides by x:
This is an exact expression for y (in terms of x). If we want a decimal approximation, we use our calculators to find that power of 10: (rounded to 4 places)
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