7-5 Properties of Logarithms
Solve each equation. Check your solutions.
36. log3 6 + log3 x = log3 12
SOLUTION: Solve for n.
42. loga 6n − 3 loga x = loga x
SOLUTION: 38. log10 18 − log10 3x = log10 2
SOLUTION: Solve each equation. Check your solutions.
44. log10 z + log10 (z + 9) = 1
SOLUTION: 40. SOLUTION: 2
46. log2 (15b − 15) – log2 (−b + 1) = 1
SOLUTION: Solve for n.
42. loga 6n − 3 loga x = loga x
SOLUTION: Substitute each value into the original equation.
log20, log2(–142.5), and log2(–71.25) are
undefined, so 1 and –8.5 are extraneous solutions.
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Therefore, the equation has no solution.
48. log6 0.1 + 2 log6 x = log6 2 + log6 5
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SOLUTION: 7-5 Properties of Logarithms
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46. log2 (15b − 15) – log2 (−b + 1) = 1
Therefore, the equation is false.
52. log5 22x = log5 22 + log5 x
SOLUTION: SOLUTION: Therefore, the equation is true.
53. log10 19k = 19 log10 k
SOLUTION: Therefore, the equation is false.
Substitute each value into the original equation.
5
54. log2 y = 5 log2 y
SOLUTION: log20, log2(–142.5), and log2(–71.25) are
Therefore, the equation is true.
undefined, so 1 and –8.5 are extraneous solutions.
Therefore, the equation has no solution.
55. 48. log6 0.1 + 2 log6 x = log6 2 + log6 5
SOLUTION: SOLUTION: Therefore, the equation is true.
56. log4 (z + 2) = log4 z + log4 2
SOLUTION: Logarithms are not defined for negative values.
Therefore, the solution is 10.
State whether each equation is true or false .
51. log8 (x − 3) = log8 x − log8 3
Therefore, the equation is false.
4
57. log8 p = (log8 p )
4
SOLUTION: SOLUTION: Therefore, the equation is false.
Therefore, the equation is false.
58. 52. log5 22x = log5 22 + log5 x
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Therefore, the equation is true.
SOLUTION: 7-5 Properties
of Logarithms
Therefore, the equation is false.
58. SOLUTION: Therefore, the equation is true.
64. CHALLENGE Simplify
to find an exact
numerical value.
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