Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Questions on manipulating logarithms.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Practice using the log rules to add and subtract logarithms

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Questions on manipulating logarithms.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Questions on manipulating logarithms.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Questions on manipulating logarithms.

Simplify logarithmic expressions using rules on logarithms.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Differentiating the natural logarithm

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Questions on manipulating logarithms.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Questions on manipulating logarithms.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Questions on manipulating logarithms.