1. Use the function \( f(x)=8(4)^{x} \) to answer the following questions. (a) Evaluate \( f(-2): \quad f(-2)= \) (b) Determine \( x \), if \( f(x)=512 \).

Use the properties of logarithms to expand the following expression. \[ \log \left(\frac{y^{7}}{\sqrt{x z^{3}}}\right) \] Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive. \( \log \left(\frac{y^{7}}{x z^{3}}\right)=\square \)

Finding a specified term of an arithmetic sequence given the common... Find the \( 19^{\text {th }} \) term of the arithmetic sequence whose common difference is \( d=5 \) and whose first term is \( a_{1}=2 \).

Find the first four terms of the sequence given by the following. \[ a_{n}=\frac{4 n}{3 n+2}, n=1,2,3, \ldots \]

Find the first four terms of the sequence given by the following. \[ a_{n}=\frac{2^{n}+1}{3^{n}}, n=1,2,3, \ldots \] n. . . . . \( \square \)

Finding a specified term of an arithmetic sequence givent Find the \( 50^{\text {th }} \) term of the following arithmetic sequence. \[ 17,26,35,44, \ldots \]