Logarithms
Evaluate , and solve exponential and equations by matching bases.
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Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
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About Logarithms
A logarithm is an exponent in disguise: log₂ 32 asks "2 to what power gives 32?", so it is 5. Every log statement can be rewritten as a power statement and back, and that switch is how most log equations get solved.
Exponential equations with the same base on both sides are solved by setting the exponents equal. When the base is 10, the log is written without a base; ln is the log with base e.
Keep in mind
- log_b(x) = y means bʸ = x.
- log_b(1) = 0 and log_b(b) = 1.
- A negative log value means a fraction: log₂(1/8) = −3.
- A fraction log value means a root: log₄ 2 = 1/2.
- Same base on both sides: bᵃ = bᶜ means a = c.
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