Question

Log 8 to the base 5 is p then log 1/40 to the base 5 is ?

Answer 1

Answer:

Originally Answered: Log 5 base (4)=a; log 6 base ( 5)=b. What is log 3 base 2? ... If log m to the base 8 +log 1/6 to the base 8=2/3, what is m? 3,188 Views

Answer 2

The value of log₅1/40 is -p-1.

Given,

The value of log₅8 = p

To Find,

The value of log₅1/40.

Solution,

The given value is

log₅8 = p

log₅1/40 = log₅(1/8*1/5)

Now, using the property of log

log(m*n) = log m + log n

So,

log₅(1/8*1/5) = log₅(1/8)+log₅(1/5)

Now, using the property

log(m/n) = log m - log n

So,

log₅(1/8)+log₅(1/5) = log₅1 - log₅8 + log₅1- log₅5

Now,

log₅1 = 0, ang log₅5 = 1

So,

log₅1 - log₅8 + log₅1- log₅5 = 0-p+-0-1 = -p-1

Hence, the value of log₅1/40 is -p-1.

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