| Solving Logarithmic Equations | Exponential Equation with Logarithms | log form to exp form (vise-versa) | Simplify each expression | Real Life Applications |
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n = 3
Solve the equation: log (n+9)=log 4n
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r = 1.0322
Solve the equation: 12^r = 13
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3^4 = 81
Rewrite the equation: log{3} 81 = 4
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log a - 2 log b
Simplify the equation: log(a/b^2)
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Magnitude of earthquake, chemistry, population growth, and economics.
Where can you find logarithms be in use in the real world?
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x = 1
Solve the equation: 7 log_{9} (x+8) = 7
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n = 2.5646
Solve the equation: 6^n = 99
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log{1/12} 1/144 = 2
Rewrite the equation: (1/2)^2 = 1/144
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log a^2 b^2/3
Simplify the equation: 2log a + 2/3log b ?
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+11.896
Suppose that $10,000 is invested at 6% interest compounded annually.In t years an investment will grow to the amount expressed by the function
S(t)=10000*1.06^t where t is time (in years). How long will it take to accumulate $20,000 in the account? |
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x = -7 and x= -2
Solve the equation: log_{15} (x^2 + 13) = log_{15} (-9x - 1)
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x= ln (10) + 1
Solve the equation: e^(x-1) - 5 = 5
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y^-8 = x
Rewrite the equation: log{y} x = - 8
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144
Simplify the equation: 12^log{12}144
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1) N(t)=N{0}^t/30
2)99.6
An initial number of bacteria presented in a culture is 10000. This number doubles every 30 minutes.
1) Write a function expressed the number of bacteria in time. 2) How long it will take to get the bacteria number 100000? |
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x = 3 and x = 5
Solve the equation: log_{19} (x^2 + 17) = log_{19} (8x + 2)
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x = 0.5704
Solve the equation: 5 x 18^6x = 26
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log{b} 123 = a
Rewrite the equation: b^a = 123
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72
Simplify the equation: x^log{x}72
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1) P(t)=P{0} x 0.5^t/138
2)458.43
Polonium Po-210 has a half-life of 138 days.
1) Write the decay function for the amount of Polonium Po-210 that remains in a sample after t days. 2) Estimate time for Polonium Po-210 to get 0.1 of its initial amount in the sample. |
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x = 4 and x= -14
Solve the equation: In (x +2) + In (x + 3) = In 77
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m = 0.2579
Solve the equation: 5 x 6^3m = 20
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log{1/5} y = x
Rewrite the equation: (1/5)^x = y
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log 8^1/6/9^1/4
Simplify the equation: 1/6 log 8 - 1/4 log 9 + 1/2 log 24
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M= Log_10(A/A_0) meant to be a image.
Early in the century the earthquake in San Francisco registered 8.3 on the Richter scale.
What is the Richter scale? |
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