### Logarithms.

is the inverse function to exponentation, as it answers the question, how many of one number do we multiply to get another number.
log_b a = (log a)/(log b)

Subjects > Mathematics > Logarithms

Question 02:

Evaluate: log_49 7 + log_8 64

###### Solution:
Given,
log_49 7 + log_8 64

we cannot use the product rule of logarithms since the terms have different bases
Now,
⇒ log_49 7 + log_8 (8^2)
⇒ log_49 7 + 2log_8 8

But, since log_a a = 1
Hence, log_8 8 = 1

⇒ log_49 7 + 2log_8 8 = log_49 7 + 2

But, log_b a = (log a)/(log b)
Hence,
⇒ (log 7)/(log 49) + 2

⇒ (log 7)/(log 7^2) + 2

⇒ (log 7)/(2log 7) + 2

⇒ 1/2 * (log 7)/(log 7) + 2

⇒ 1/2 * log_7 7 + 2
Again, log_7 7 = 1
Hence,
⇒ 1/2 * 1 + 2 = 2 1/2 = 2.5

∴ log_49 7 + log_8 64 = 2.5

Sorry, it's under construction !

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Question 02:

Evaluate: log_49 7 + log_8 64

###### Solution:
Given,
log_49 7 + log_8 64

we cannot use the product rule of logarithms since the terms have different bases
Now,
⇒ log_49 7 + log_8 (8^2)
⇒ log_49 7 + 2log_8 8

But, since log_a a = 1
Hence, log_8 8 = 1

⇒ log_49 7 + 2log_8 8 = log_49 7 + 2

But, log_b a = (log a)/(log b)
Hence,
⇒ (log 7)/(log 49) + 2

⇒ (log 7)/(log 7^2) + 2

⇒ (log 7)/(2log 7) + 2

⇒ 1/2 * (log 7)/(log 7) + 2

⇒ 1/2 * log_7 7 + 2
Again, log_7 7 = 1
Hence,
⇒ 1/2 * 1 + 2 = 2 1/2 = 2.5

∴ log_49 7 + log_8 64 = 2.5

Sorry, it's under construction !

Skills covered in the above question

Related Lessons