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Published byChristiana Stewart
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Find the value of y such thatlog2 y= –3 Find the positive value of x such that logx 64 = 2
We can simplify logs in the same way we simplify indicesloga (xy) = logax + logay loga x = logax – logay y loga1/x = -loga x loga xn = nlogax logaa = 1 and loga1 = 0
Example Write as a single log log36 + log37 2log53 + 3log52Note : like indices, they must have the same base!
Solving We can solve exponential equations by using logs Solve, 3x = 20
Example 1 Solve 7x+1 = 3x+2
Example 2 Solve 52x + 7(5x) – 30 = 0
Example 3 Solve the equation log3(5x-1) - log3(x+1) = 1
May 2007 qu 6 (a) Find, to 3 significant figures, the value of x for which 8x = 0.8. (2) (b) Solve the equation 2 log3 x – log3 7x = 1 (4)
Jan 08 qu 5 Given that a and b are positive constants, solve the simultaneous equations a = 3b, log3a + log3b = 2. Give your answers as exact numbers. (6)
Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.
Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.
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EXAMPLE 5 Write a joint variation equation The variable z varies jointly with x and y. Also, z = –75 when x = 3 and y = –5. Write an equation that relates.
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LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”
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Solve the equation -3v = -21 Multiply or Divide? 1.
4.4 Solving Exponential and Logarithmic Equations.
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1 Integrated Mathematics Solving Exponential Equations.
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Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334.
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C2: Solving Equations with Logarithms Learning Objective: to be able to solve equations of the form a x = b.
Solving Log Equations We will be using all of the properties. You will have to figure out which ones to use and when to use them. You will have.
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