How to Solve Logarithms
Know the logarithm definition., Look at the equation., Move the exponential expression to one side of the equation., Apply the exponent to the base., Rewrite your final answer.
Step-by-Step Guide
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Step 1: Know the logarithm definition.
Before you can solve logarithms, you need to understand that a logarithm is essentially another way to write an exponential equation.
It's precise definition is as follows: y = logb (x) If and only if: by = x Note that b is the base of the logarithm.
It must also be true that: b > 0 b does not equal 1 In the same equation, y is the exponent and x is the exponential expression that the logarithm is set equal to. , When looking at the problem equation, identify the base (b), exponent (y), and exponential expression (x).
Example: 5 = log4(1024) b = 4 y = 5 x = 1024 , Set the value of your exponential expression, x, to one side of the equal sign.
Example: 1024 = ? , The value of your base, b, needs to be multiplied by itself by the amount of times indicated by your exponent, y.
Example: 4 * 4 * 4 * 4 * 4 = ? This could also be written as: 45 , You should be able to rewrite the logarithm as an exponential expression now.
Verify that your answer is correct by making sure that both sides of the equation are equal.
Example: 45 = 1024 -
Step 2: Look at the equation.
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Step 3: Move the exponential expression to one side of the equation.
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Step 4: Apply the exponent to the base.
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Step 5: Rewrite your final answer.
Detailed Guide
Before you can solve logarithms, you need to understand that a logarithm is essentially another way to write an exponential equation.
It's precise definition is as follows: y = logb (x) If and only if: by = x Note that b is the base of the logarithm.
It must also be true that: b > 0 b does not equal 1 In the same equation, y is the exponent and x is the exponential expression that the logarithm is set equal to. , When looking at the problem equation, identify the base (b), exponent (y), and exponential expression (x).
Example: 5 = log4(1024) b = 4 y = 5 x = 1024 , Set the value of your exponential expression, x, to one side of the equal sign.
Example: 1024 = ? , The value of your base, b, needs to be multiplied by itself by the amount of times indicated by your exponent, y.
Example: 4 * 4 * 4 * 4 * 4 = ? This could also be written as: 45 , You should be able to rewrite the logarithm as an exponential expression now.
Verify that your answer is correct by making sure that both sides of the equation are equal.
Example: 45 = 1024
About the Author
Hannah Jones
Hannah Jones is an experienced writer with over 2 years of expertise in finance and banking. Passionate about sharing practical knowledge, Hannah creates easy-to-follow guides that help readers achieve their goals.
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