# Mathematics

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4. Solve:

a Solve for x if 2logx = 2 + log25

b Simplify log3 81 - log3 27 + 4log3 v3

c Find the inverse of the function f(x) = e^x + 1

5. This is completing a piecewise function which consists of 2 straight lines and a parabola.

Coordinates given are (-6,0) (-3,6)-straight line, (-3,6) (.5, -6) (2,-4) -parabola, and last straight line (2,-4) parallel to x-axis

Need equation and domain for each piece

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Solution1a:

Given: 2logx = 2 +log25

log100 = 2 [Since, log100 = log102 = 2log10 =2]

Therefore,

2logx = log100 +log25

Using power law of logarithms, 2log(x) = log(x2)

Therefore,

log(x2) = log(25) + log(100)

Using sum rule for logarithms, log(25) + log(100) = log(25x100):

log(x2) = log(2500)

Removing all logarithms (by raising everything to the power of 10):

x2= 2500

Or, x = +/- 50

Since 2log(-50) doesn't exist, therefore x = +50

Solution1b:

log3 81 = log81/log3 [Using the change of base rule for logarithms]

= log 34/log3

= 4log3/log3 [Using power law of ...

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