# Given that log 10(7)=.8450, what is log 7(0.01)?

### 3 Answers | Add Yours

Here we are given that log 10 (7) = 0.8450 and we have to find log 7 (0.01).

We first use the relation that log x^n = n log x.

Therefore log 7 (0.01) = log 7(10^-2) = -2*log 7(10).

Now we use the relation that log a (X) = log b(X) / log b (a). This can be used to change the base of the logarithm.

So log 7(10) = log 10(10) / log 10(7) = 1/ 0.8450 = 1.1832

=> -2* log 7(10) = -2.3665

**Therefore log 7(0.01) is approximately equal to -2.3665.**

Given that:

log 7 = 0.8450

We need to calculate log 7 (0.01)

We will algorethim properties:

First we will rewrtie :

0.01 = 1/100 = 10^-2

==> log 7 ( 0.01) = log 7 ( 10)^-2

We know that: log a^b = b*log a

==> log 7 (0.01) = - 2log 7 10

Now we can rewrtie:

log a b = log c b / log c a

==> log 7 ( 0.01) = -2 log 10 10/ log 10 7

= -2/ 0.8450

= -2.37 ( approx.)

**==> log 7 ( 0.01) = -2.37 **

log10(7) = 0.8490

To find log7 (0.01).

We know that If loga (b) = log C(b)/logc (a)

Therefore log 7 (0.01) = log 10 (0.01)/ log10 (7)

log7(0.01) = log 10 (10 ^(-2))/ log 10 (7).

log7(0.01) = -2/ log10 (7)

log7(0.01) = -2/0.8450

log7 (0.01) = -2.3669.

Therefore log 7 (0.01) = **-2.3669** , if log 10(7) is 0.8450.