You can
put this solution on YOUR website!Given to solve for x:
.
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Take the base 10 logarithm of both sides:
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Apply the rule of logarithms that says an exponent comes out as the multiplier of the logarithm.
When you apply that rule, the problem becomes:
.
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But your calculator will tell you that
and
Make these two substitutions into the equation and it becomes:
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which simplifies to:
.
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subtract 5x - 3 from both sides to get the equation into the standard form of:
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The left side of this equation factors to give:
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Notice that this equation will be true if either of the two factors is equal to zero ... because
a multiplication by zero on the left side makes the entire left side equal to zero and
therefore equal to the right side.
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So either
or
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Solve these two equations. From
you can see that
and from
you get
.
Therefore, the two answers to this problem are x = 1 and x = 1.5
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Hope this helps you to understand the problem and how it can be worked to get the answer.
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