6.4 Logarithms practice 3

[math]12^{-\log_{12}144}=[/math]

If [math]\log_{3}x-\log_{3}y=3[/math], then [math]\displaystyle{\frac{x}{y}}=[/math]

Let [math]a=\log_{2}3, b=\log_{2}5[/math], find [math]\log_{2}75[/math] in terms of [math]a[/math] and [math]b[/math].

Evaluate the following logarithms.

(a) [math]\log_{\sqrt[3]{32}}(16\sqrt{2})[/math]

(b) [math]e^{6\ln\sqrt{e}}[/math]

Simplify the following logarithms. If the logarithm is undefined, write “undef”

(a) [math]\log\left(-\displaystyle{\frac{1}{2}}\right)[/math]

(b) [math]3\ln e^y[/math]

(c) [math]\log_{\pi}1[/math]

Given [math]f(x)=\log_{5}x[/math], find the following and simplify your answer:

(a) [math]f(125)[/math]

(b) [math]f(\sqrt{5})[/math]

Let [math]a=\log2, b=\log3[/math] and [math]c=\log5[/math]. Express [math]\log_{9}200[/math] in terms of [math]a, b[/math], and [math]c[/math].