Exercise 24 Page 327

a We are given the following equation.

lo g_{2} (3) = x

We want to rewrite it so that we only use

lo g_{10}

— common logarithms. We will use the Change of Base Formula to evaluate the given expression.

lo g_{b} m = \frac{lo g _{c} m}{lo g _{c} b}

In the above formula

m,

b,

and

c

are positive numbers, with

b \neq = 1

and

c \neq = 1 .

We will apply this formula to our expression.

lo g_{2} (3) = \frac{lo g _{10} ( 3 )}{lo g _{10} ( 2 )}

Let's use the found expression to rewrite the given equation.

lo g_{2} (3) = x \Leftrightarrow \frac{lo g _{10} ( 3 )}{lo g _{10} ( 2 )} = x

b We are given the following equation.

lo g_{5} (8) = x

We want to rewrite it so that we only use

lo g_{10}

— common logarithms. We will use the Change of Base Formula to evaluate the given expression.

lo g_{b} m = \frac{lo g _{c} m}{lo g _{c} b}

In the above formula,

m,

b,

and

c

are positive numbers, with

b \neq = 1

and

c \neq = 1 .

We will apply this formula to our expression.

lo g_{5} (8) = \frac{lo g _{10} ( 8 )}{lo g _{10} ( 5 )}

Let's use the found expression to rewrite the given equation.

lo g_{5} (8) = x \Leftrightarrow \frac{lo g _{10} ( 8 )}{lo g _{10} ( 5 )} = x

c We are given the following equation.

lo g_{7} (12) = x

We want to rewrite it so that we only use

lo g_{10}

— common logarithms. We will use the Change of Base Formula to evaluate the given expression.

lo g_{b} m = \frac{lo g _{c} m}{lo g _{c} b}

In the above formula

m,

b,

and

c

are positive numbers, with

b \neq = 1

and

c \neq = 1 .

We will apply this formula to our expression.

lo g_{7} (12) = \frac{lo g _{10} ( 1 2 )}{lo g _{10} ( 7 )}

Let's use the found expression to rewrite the given equation.

lo g_{7} (12) = x \Leftrightarrow \frac{lo g _{10} ( 1 2 )}{lo g _{10} ( 7 )} = x

d We are given the following equation.

lo g_{a} (b) = x

We want to rewrite it so that we only use

lo g_{10}

— common logarithms. We will use the Change of Base Formula to evaluate the given expression.

lo g_{b} m = \frac{lo g _{c} m}{lo g _{c} b}

In the above formula

m,

b,

and

c

are positive numbers, with

b \neq = 1

and

c \neq = 1 .

We will apply this formula to our expression.

lo g_{a} (b) = \frac{lo g _{10} ( b )}{lo g _{10} ( a )}

Let's use the found expression to rewrite the given equation.

lo g_{a} (b) = x \Leftrightarrow \frac{lo g _{10} ( b )}{lo g _{10} ( a )} = x

7.1.1 Using Logarithms to Solve Exponential Equations p.323

7.1.2 Investigating the Properties of Logarithms p.327-328

7.1.3 Writing Equations of Exponential Functions p.331-332

7.1.4 An Application of Logarithms p.336-337