High School

Express the equation in exponential form:

(a) log_2 16 = 4. That is, write your answer in the form 2^A = B. Then
A =
B =

(b) log_5 3125 = 5. That is, write your answer in the form 5^C = D. Then
C =
D =

Answer :

To express logarithmic equations in exponential form, we can use the basic property that relates logarithms and exponents: if [tex]\log_b A = C[/tex], then [tex]b^C = A[/tex]. Let's apply this to the given problems.

(a) Convert [tex]\log_2 16 = 4[/tex] to exponential form:

Here, the base [tex]b = 2[/tex], the logarithm equals [tex]C = 4[/tex], and inside the log [tex]A = 16[/tex].

Using the property, we write:

[tex]2^4 = 16[/tex]

So, [tex]A = 4[/tex] and [tex]B = 16[/tex]. This means:


  • [tex]A = 4[/tex]

  • [tex]B = 16[/tex]


(b) Convert [tex]\log_5 3125 = 5[/tex] to exponential form:

Here, the base [tex]b = 5[/tex], the logarithm equals [tex]C = 5[/tex], and inside the log [tex]A = 3125[/tex].

Using the property, we write:

[tex]5^5 = 3125[/tex]

So, [tex]C = 5[/tex] and [tex]D = 3125[/tex]. This means:


  • [tex]C = 5[/tex]

  • [tex]D = 3125[/tex]


By understanding how to express logarithms in exponential form, you can make it much easier to solve problems involving growth, decay, and other exponential models.

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