CPM Homework Help : A2C Problem 6-73

Every exponential equation has an equivalent logarithmic form and every logarithmic equation has an equivalent exponential form. For example, First Equation, 4 raised to the third, = 64, with 4 labeled, base, 3 labeled, exponent. Second equation: 3 = log, base 4, of 64, with 3 labeled, exponent, & 4 labeled, base. Between equations is title "is equivalent to".
Copy the table shown below and fill in the missing form in each row.

	Exponential Form	Logarithmic Form
a.	$y=5^x$
b.		$y=\log_7\left(x\right)$
c.	$8^x=y$
d.	$\text{A}^\text{K} = \text{C}$
e.		$\text{K}=\log_\text{A}(\text{C})$
f.		$\log_{1/2}(\text{K}) = \text{N}$

Answer:

	Exponential Form	Logarithmic Form
a.	$y=5^x$	${\color{red}{x=\log_5\left(y\right)}}$
b.	${\color{red}{x=7^y}}$	$y=\log_7\left(x\right)$
c.	$8^x=y$	${\color{red}{x=\log_8\left(y\right)}}$
d.	$\text{A}^\text{K} = \text{C}$	${\color{red}{\text{K}=\log_A(\text{C})}}$
e.	${\color{red}{C=A^K}}$	$\text{K}=\log_\text{A}(\text{C})$
f.	${\color{red}{K=({\frac{1}{2}})^N}}$	log $_{1/2}$ (K) = N