Logs Review/Practice

Logs Review/Practice If “x” is the argument of a log, and “b” is the base of a log, then: logb x = y  by = x The natural log of x, is the log “base e” of x (written either loge x or ln x): ln x = y  ey = x Logs and exponential functions are inverses (e.g., “undo” each other) A “log” is an exponent. Specifically, it’s the exponent of the base that yields the argument of the log. e is a special number (like p), having a value of 2.7182… (non- repeating decimal) eln x = x ln (ex) = x eln (-3x) = -3x ln (ebz) = bz

Logs Review/Practice Solve for x: b = e-ax Solve for x: ln x = b   ln b = ln e-ax   eln x = eb   ln b = -ax   x = eb   ln b = x  -a

Logs Review/Practice ln a + ln b Simplify: ln(ab) = Simply: ln(bc) = c ln b

Logs Review/Practice Solve for x by taking the ln of both sides: d = Aebx   ln d = ln Aebx   ln d = ln A + ln ebx   ln d = ln A + bx   ln d - ln A = bx b   ln d - ln A = x

Logs Review/Practice Solve for m: 7.8 = 2.0m   ln 7.8 = ln 2.0m   ln 7.8 = m ln 2.0   m = 2.96…