What is the value of log 625 5

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Algebra

Evaluate log base 625 of 5

Step 1

Rewrite as an equation.

Step 2

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and does not equal , then is equivalent to .

Step 3

Create expressions in the equation that all have equal bases.

Step 4

Rewrite as .

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

Step 6

Solve for .

Step 7

The variable is equal to .

Step 8

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Click here to see ALL problems on Exponential-and-logarithmic-functions Question 974057: log base 625 of exponent 5=??? A)4 B)8 c)1/4 D)1/8 Found 2 solutions by larrypizzu , Alan3354: Answer by larrypizzu (5)     (Show Source): You can put this solution on YOUR website! Answer is C Answer by Alan3354(68931)     (Show Source): You can put this solution on YOUR website! log base 625 of exponent 5=??? -------------------- log base 625 of 5: No reason to mention exponent. --- ================= Or, use the base change formula:

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value of =log 625√5

Question

value of = log625√5

A

4

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B

8

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C

14

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D

18

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Solution

The correct option is C 18log625√5 = log625 62518 =18log625625 18

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