Question

Write the equation in exponential form. Assume that all constants are positive and not equal to 1.

Answer 1

Answer:

1.     $16 = 4^2$

2.    $2 = {16}^{\frac{1}{4}}$

3.    $log_2 y=z$

Step-by-step explanation:

$1.\ log_2 16=4$

Write in exponential form

Using the law of logarithm which says if

$log_b A=x$

then

$A = b^x$

By comparison;

A = 16; b = 2 and x = 4

The expression $log_2 16=4$ becomes

$16 = 4^2$

$2.\ log_{16} 2=\frac{1}{4}$

Write in exponential form

Applying the same law as used in (1) above;

A = 2; b = 16 and $x = \frac{1}{4}$

The expression $log_{16} 2=\frac{1}{4}$ becomes

$2 = {16}^{\frac{1}{4}}$

$3.\ 2^z=y$

Write in logarithm form

Using the law of logarithm which says if

$b^x =A$

then

$log_b A=x$

By comparison;

b = 2; x = z and A = y

The expression $2^z=y$ becomes

$log_2 y=z$