How do you evaluate log_625 25?

2 Answers
Alan P.
Sep 1, 2016

log_625 25 = color(green)(1/2)

Explanation:

Note that 625 = 25^2color(white)("XX")rarr 25 = 625^(1/2)

Therefore
color(white)("XXX")log_625 25 = log_625 626^(1/2)

color(white)("XXX")rarr log_625 25 = 1/2 (by definition of log)

EZ as pi
Sep 1, 2016

log_625 25 = 1/2

Explanation:

Logs are easier to understand if you think about an expression given in log form as asking a question.

In log_625 25, the question being asked is;

"What power/index of 625 will give 25?"
OR " How do I make 625 into 25?"

You should recognise 25 as being the square root of 625.

A square root can be written as an index.

sqrtx = x^(1/2)

sqrt625 = 625^(1/2) larr this answers our question!

log_625 25 = 1/2

Log form and index form are interchangeable.

log_a b = c hArr a^c = b

log_625 25 = x hArr 625^x = 25

625^x = (25^2)^x= 25^1 larr make the bases the same

25^(2x) = 25^1 larr equate the indices and solve for x

2x = 1 rarr x = 1/2

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