Answer:
1. [tex]16 = 4^2[/tex]
2. [tex]2 = {16}^{\frac{1}{4}}[/tex]
3. [tex]log_2 y=z[/tex]
Step-by-step explanation:
[tex]1.\ log_2 16=4[/tex]
Write in exponential form
Using the law of logarithm which says if
[tex]log_b A=x[/tex]
then
[tex]A = b^x[/tex]
By comparison;
A = 16; b = 2 and x = 4
The expression [tex]log_2 16=4[/tex] becomes
[tex]16 = 4^2[/tex]
[tex]2.\ log_{16} 2=\frac{1}{4}[/tex]
Write in exponential form
Applying the same law as used in (1) above;
A = 2; b = 16 and [tex]x = \frac{1}{4}[/tex]
The expression [tex]log_{16} 2=\frac{1}{4}[/tex] becomes
[tex]2 = {16}^{\frac{1}{4}}[/tex]
[tex]3.\ 2^z=y[/tex]
Write in logarithm form
Using the law of logarithm which says if
[tex]b^x =A[/tex]
then
[tex]log_b A=x[/tex]
By comparison;
b = 2; x = z and A = y
The expression [tex]2^z=y[/tex] becomes
[tex]log_2 y=z[/tex]
The given equations written in exponential or logarithmic form as the case is is;
1) 2⁴ = 16
2)16^(¼) = 2
3) Log_2_y = z
Usually in logarithmic exponential functions expressions;
When we have;
Log_n_Y = 2
It means that; n² = Y
Applying that same principle to our question means that;
1) log_2_16 = 4
This will now be;
2⁴ = 16
2) log_16_2 = ¼
This will now be;
16^(¼) = 2
3) For 2^(z) = y
We have;
Log_2_y = z
Read more about properties of logarithmic exponents at; https://brainly.com/question/10005276
