Solve each logarithmic equation.
Q14. $\displaystyle x=\log_8 \sqrt[4]{8}$
Q20. $\displaystyle x=12^{\log_{12}5}$
Q24. $\displaystyle \log_x {1 \over 16}=-2$
Sketch the graph of $f(x)=\log_2 x$. Then refer to it to graph these functions.
Q34. $\displaystyle f(x)=\log_2(x+3)$
Q42. $\displaystyle f(x)=\log_2{x\over 2}$
Q50. Sketch the graph $\displaystyle f(x)=\log_2x^2$
Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers.
Q58. $\displaystyle \log_3{4p\over q}$
Q61. $\displaystyle \log_4{2x+5y}$
Q64. $\displaystyle \log_p\sqrt[3]{{m^5 n^4\over t^2}}$
Write each expression as a single logarithm with coefficient $1$. Assume all variables represent positive real numbers.
Q66. $\displaystyle (\log_bk-\log_bm)-\log_ba$
Q68. $\displaystyle {1\over 2} \log_yp^3q^4 -{2\over 3} \log_y p^4q^3$
Q70. $\displaystyle \log_b(2y+5)-{1\over 2} \log_b(y+3)$
Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers.
Q58. $\displaystyle \log_3{4p\over q}$
Q61. $\displaystyle \log_4{2x+5y}$
Q64. $\displaystyle \log_p\sqrt[3]{{m^5 n^4\over t^2}}$
Write each expression as a single logarithm with coefficient $1$. Assume all variables represent positive real numbers.
Q66. $\displaystyle (\log_bk-\log_bm)-\log_ba$
Q68. $\displaystyle {1\over 2} \log_yp^3q^4 -{2\over 3} \log_y p^4q^3$
Q70. $\displaystyle \log_b(2y+5)-{1\over 2} \log_b(y+3)$
SOLUTIONS ==================
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