99.8k views
0 votes
6log6(36)
simplify with logarithmic properties

User KinoP
by
7.6k points

2 Answers

3 votes

Final answer:

The expression 6log6(36) simplifies to 12, using the logarithmic property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, combined with the fact that log base b of b is always 1.

Step-by-step explanation:

To simplify 6log6(36) using logarithmic properties, we should identify that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. In this case, the base of the logarithm and the base of the number inside the logarithm are the same, which simplifies the expression significantly.

Firstly, 36 is a power of 6, since 36 = 62. So, we can write the expression as 6log6(62). Applying the logarithmic property that logb(an) = n · logb(a), we get 6 · 2 · log6(6). Since logb(b) is always 1, the expression further simplifies to 6 · 2 · 1, which equals 12.

Therefore, 6log6(36) simplifies to 12.

User Nikhileshwar
by
7.6k points
2 votes

6log6(36)

log6(36) is the same as 6^x = 36

Since 6^2 = 36, x=2 and log6(36)=2.

So, 6log6(36)=2x6=12

answer: 12

User Norio Akagi
by
7.7k points

Related questions

asked Jan 4, 2021 90.9k views
Lanston asked Jan 4, 2021
by Lanston
8.2k points
1 answer
3 votes
90.9k views
asked May 21, 2021 221k views
Alanl asked May 21, 2021
by Alanl
8.1k points
1 answer
0 votes
221k views
asked Aug 22, 2023 72.3k views
Gepser Hoil asked Aug 22, 2023
by Gepser Hoil
8.3k points
1 answer
22 votes
72.3k views