Express as the logarithm of a single quantity 3. log 3+ 2 log: y 4, 2 log, x +5l

Question

Express as the logarithm of a single quantity 3. log 3+ 2 log: y 4, 2 log, x +5log, 3 log, m Determine the exact value of each of the given logarithms. 6. log V16 5. log, 49 7. -2 log, 9 Express as a sum, difference, or multiple of logarithms. In each problem, part of the logarithm may be determined exactly. log, V12 9. log, 48 10, log, 250 63. Simplify: logMI b logull t b 2') as a single logMWhm. 64. If f(r) logb x, express W 65. On the same screen of a calculator, display the graphs of What logio a single quantity: conclusion can be drawn from the display? irir DDT was banned in the United States in

Explanation / Answer

Log Rules

1) logb(mn) = logb(m) + logb(n)

2) logb(m/n) = logb(m) – logb(n)

3) logb(mn) = n · logb(m)

so

( 3 )

1) log2(3) +2 log2(y)

==> log2(3) + log2(y^2)

==> log2(3y^2)

( 4 ) 2 log7(x) +5 log7(y) - 3 log7(m)

==> log7(x^2) + log7(y^5) - log7(m^3)

==> log7(x^2y^5) - log7(m^3)

==> log7(x^2y^5 / m^3 )

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