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Definition of a logarithm log_b(x) = y means bʸ = x math-log-rules
Product rule log_b(xy) = log_b x + log_b y math-log-rules
Quotient rule log_b(x/y) = log_b x − log_b y math-log-rules
Power rule log_b(xⁿ) = n log_b x math-log-rules
Change of base log_b x = log x / log b (any base) math-log-rules
Log of 1 log_b 1 = 0 math-log-rules
Log of the base log_b b = 1 math-log-rules
Inverse property 1 b^(log_b x) = x math-log-rules
Inverse property 2 log_b(bˣ) = x math-log-rules
Common logarithm Base 10, written log x math-log-rules
Natural logarithm Base e, written ln x math-log-rules
Binary logarithm Base 2, written log₂ x math-log-rules
Domain of log x x > 0 math-log-rules
log of a negative number Not defined among the real numbers math-log-rules
log 100 2 math-log-rules
log 1,000 3 math-log-rules
log 0.1 −1 math-log-rules
log 0.01 −2 math-log-rules
log 10 1 math-log-rules
log₂ 8 3 math-log-rules
log₂ 64 6 math-log-rules
log₂ 1024 10 math-log-rules
log₃ 81 4 math-log-rules
log₅ 125 3 math-log-rules
log₄ 2 1/2 math-log-rules
log₂ (1/8) −3 math-log-rules
ln e 1 math-log-rules
ln 1 0 math-log-rules
ln(e²) 2 math-log-rules
e^(ln 5) 5 math-log-rules
Expand log(ab/c) log a + log b − log c math-log-rules
Condense 2 log x + log y log(x²y) math-log-rules
Solve 2ˣ = 16 x = 4 math-log-rules
Solve 3ˣ = 5 x = log 5 / log 3 (about 1.465) math-log-rules
Solve log₂ x = 5 x = 32 math-log-rules
Is log(x + y) = log x + log y? No. The product rule needs log(xy) math-log-rules
Is log(x)/log(y) the same as log(x/y)? No. They are different quantities math-log-rules
Graph of y = log x: vertical asymptote x = 0 math-log-rules
Graph of y = log x: x-intercept x = 1 math-log-rules
Value of e (to 5 decimals) 2.71828 math-log-rules
Half-life formula idea Amount = start × (1/2)^(t / half-life) math-log-rules
Decibel scale uses A logarithm of a power ratio (10 log₁₀) math-log-rules
Richter scale uses A base-10 logarithm of shaking amplitude math-log-rules
pH formula pH = −log₁₀[H⁺] math-log-rules