Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Logarithmic and Exponential Functions, Exercise 4: EXERCISE 2C

Write as a single logarithm, then simplify your answer.

${\log }_{2}40-{\log }_{2}5$

Given that $y={\log }_{5}x,$ find in terms of $y:$

${\log }_5\left(25x\right)$

Given that $x={\log }_{4}p$ and $y={\log }_{4}q,$ express in terms of $x$ and/or $y:$

${\log }_4\left(64p\right)$

Given that ${\log }_{a}x=7$ and ${\log }_{a}y=4,$ find the value of:

${\log }_a\left(\frac{x}{y}\right)$

Given that ${\log }_{a}x=7$ and ${\log }_{a}y=4,$ find the value of:

${\log }_a\left(\frac{\sqrt{x}}{y^2}\right)$

Given that ${\log }_{a}x=7$ and ${\log }_{a}y=4,$ find the value of:

${\log }_a\left(x^2\sqrt{y}\right)$

Given that ${\log }_{a}x=7$ and ${\log }_{a}y=4,$ find the value of:

${\log }_a\left(\frac{y}{\sqrt[3]{x}}\right)$

The number in the rectangle on the side of the triangle is the sum of the numbers at the adjacent vertices.

For example, $x+y=-{\log }_{2}5$

Find the value of $x,$ the value of $y$ and the value of $z.$