Exponential & Logarithmic Equations Part 2

Solving Logarithmic Equations steps:

1.   Place one logarithm with base 10 on each side of the equation.

2.   Using the Laws of Logarithms move the exponents the front of each logarithm. If the exponent contains a binomial we must use brackets around the exponent.

3.  If the exponent is in the brackets, multiply through brackets.

4.  Collect logarithms on one side and isolate the variable on the others. If there is more than one term containing the missing variable isolate these terms on one side and factor out the variable, then continue to isolate the variable.

5.    Solve for the variable using your calculator rounding to whatever decimal place the question instructs.

6.   Check your answer! Plug your answer back into the original question and check.

Example 1: Solve to the nearest ten-thousandth.

a, 2^x =45                          b, 5^x = 3 ^x-4

log 2^x =  log45                   log 5^x = log 3 ^x-4

xlog2 = log45                   xlog5 = (x-4) log3

x   = log₂45                    xlog5 = xlog3-4log3

x = 5.4918                      xlog5-xlog3 = -4log3

                                     x(log5-log3)= -4log3

                                    x    = (-4log3)/(log5-log3)

                                                x    = -8.6

c, 3^2x+1 = 100                               d, 3 ^x+1 = 7 ^x-1 .3
log 3^2x+1 = log100                  log 3 ^x+1 = log 7 ^x-1 .3
(2x+1)log3 = 2                    (x+1)log3 = (x-1) log7 +log3
2xlog3 +log3 =2              xlog3+log3 = xlog7 – log7 + log3
2xlog3 = 2 - log3            xlog3-xlog7 = log 3 – log3 – log 7
                                     x(log3 – log7) = -log7 X= 2 – log3                                                                                                                                                                                  x = -log7/ (log3- log7)
X = 1.5959                             x= 2.2966.

-JAN PHAM-