Chapter 4

Chapter 4

1. 4.1 Logarithmic functions

   • Log_aX=Y
   • a^y=x

2. 4.2 Laws of logarithms

   • log_b(mn)= log_b(m) + log_b(n)
   • log_b(m/n) = log_b(M) - log_b(n)
   • log_b(m^n) = nlog_b(m)

3. 4.3 Logarithmic scales

   • pH=-log[H^+)
   • B=10log(I/I) where I^0=10^-12
   • M=log(I/s)

4. 4.4 Natural exponential & logarithmic functions

   • natural exponential function ----> f(x)=e^x
   • Natural exponential ----> f(x)= ln(x) = log_e(x)
   • ln(e^10) = log_ee^10 = 10
   • e^ln(x) = log_ex= ln(x) x=1

5. 4.5 exponential equation: getting info from a model

   • 2^x=16 == log _216=x
   • 3^x= 15(7)^x --> (3/7)^x=15 --> log_3/7 15=x