Question

we know that log base 10 100000 = 5 show that you get the same answer by writing 100000 = 1000 × 100 and then using product rule. verify the answer ​

Answer 1

Step-by-step explanation:

Given :

To prove,

$log_{10}100000 = 5$,

since, 100000 = 100 × 1000,.

Then,

⇒$log_{10}1000 + log_{10}100 = 5$

Solution :

Proof :

$log_{10}100000 = log_{10}10^5 = 5log_{10}10 = 5\times 1 = 5$

We know that,

$log_{A}B + log_{A}C = log_{A}(B\times C)$ (product rule)

Hence,

we know that,

$10^5 = 10^2 \times 10^3$,

$100000 = 1000 \times 100$,

Hence,

by product rule,

$log_{10}100 = log_{10}10^2 = 2log_{10}10 = 2\times 1 = 2$

$log_{10}1000 = log_{10}10^3 = 3log_{10}10 = 3\times 1 = 3$

⇒$log_{10}1000 + log_{10}100 = log_{10}(100 \times 1000) = log_{10}100000$

$log_{10}100000 = log_{10}1000 + log_{10}100$

Hence, proved.

Answer 2

Answer:

Step-by-step explanation:

Given :

To prove,

log_{10}100000 = 5,

since, 100000 = 100 × 1000,.

Then,

⇒log_{10}1000 + log_{10}100 = 5

Solution :

Proof :

log_{10}100000 = log_{10}10^5 = 5log_{10}10 = 5\times 1 = 5

We know that,

log_{A}B + log_{A}C = log_{A}(B\times C) (product rule)

Hence,

we know that,

10^5 = 10^2 \times 10^3,

100000 = 1000 \times 100,

Hence,

by product rule,

log_{10}100 = log_{10}10^2 = 2log_{10}10 = 2\times 1 = 2

log_{10}1000 = log_{10}10^3 = 3log_{10}10 = 3\times 1 = 3

⇒log_{10}1000 + log_{10}100 = log_{10}(100 \times 1000) = log_{10}100000

log_{10}100000 = log_{10}1000 + log_{10}100

Hence, proved.