2.12 · Logarithmic Function Manipulation

Try each one on paper first, then tap to check.

1. 1.

   Write as a sum or difference of logarithms ($x,y>0$): $\log_3(xy^3)$
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2. 2.

   Write as a sum or difference of logarithms ($x,y>0$): $\ln\dfrac{x^2}{y^3}$
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3. 3.

   Write as a sum or difference of logarithms ($x,y>0$): $\log(1000x^3)$
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4. 4.

   Write as a sum or difference of logarithms ($x,y>0$): $\log_2(8\sqrt{x})$
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5. 5.

   Write as a sum or difference of logarithms ($x,y>0$): $\log_2\sqrt{\dfrac{16x^3}{y^2}}$
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6. 6.

   Write as a sum or difference of logarithms ($x,y>0$): $\log_3(9x-27)$
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7. 7.

   Write as a single logarithm ($x,y>0$): $\ln 3+\ln x$
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8. 8.

   Write as a single logarithm ($x,y>0$): $2\log_3 x-4\log_3 y$
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9. 9.

   Write as a single logarithm ($x,y>0$): $\frac12(\log x+3\log y)$
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10. 10.

    Write as a single logarithm ($x,y>0$): $3\log_5(x-4)-2\log_5 y$
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11. 11.

    Change to base 10 or $e$, then evaluate to the nearest thousandth: $\log_4 123$
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12. 12.

    Change to base 10 or $e$, then evaluate to the nearest thousandth: $\log_9 578$
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13. 13.

    Describe the transformations, then find the domain and range: $f(x)=\log_4(16x)$
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14. 14.

    Describe the transformations, then find the domain and range: $g(x)=\log_2\left(\dfrac{x}{8}\right)$
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15. 15.

    Describe the transformations, then find the domain and range: $f(x)=\log_5 x^2$
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16. 16.

    Describe the transformations, then find the domain and range: $h(x)=\log_2(32-16x)$
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