Question

Log6 (108) + log6 12-1

Answer 1

Ответ:

Объяснение:

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Answer 2

108=2*2*3*3*3

108=2²*3³

12=2²*3

(㏒₆108+㏒₆12)-1=㏒₆(108*12)-1=㏒₆(2⁴*3⁴)-1=㏒₆(6⁴)-1=4*㏒₆6-1=4-1=3

Answer 3

To solve the expression:

log₆(108) + log₆(12^(-1))

You can use the properties of logarithms to simplify it. The first term, log₆(108), can be further simplified by factoring 108 into its prime factors:

108 = 2^2 * 3^3

Now, we can use the properties of logarithms to simplify the expression:

log₆(108) + log₆(12^(-1)) = log₆(2^2 * 3^3) + log₆(1/12)

Now, we can use the properties of logarithms to combine the terms:

log₆(2^2 * 3^3 * 1/12)

Using the properties of logarithms, you can combine the terms inside the logarithm:

log₆(2^2 * 3^3 * 1/12) = log₆((2^2 * 3^3) / 12)

Now, we can simplify the expression inside the logarithm:

2^2 = 4 3^3 = 27

So, the expression becomes:

log₆((4 * 27) / 12)

Now, simplify the expression inside the logarithm:

(4 * 27) / 12 = 108 / 12 = 9

So, the expression becomes:

log₆(9)

Now, you can evaluate the logarithm:

log₆(9) = 2

So, the final result is:

log₆(108) + log₆(12^(-1)) = 2

Answer 4

To simplify the expression "log₆(108) + log₆(12⁻¹)," you can use logarithmic properties. First, let's work with each term separately:

1. log₆(108):

   You can simplify this by finding the prime factorization of 108:

   108 = 2² * 3³

   Now, you can use logarithmic properties to simplify:

   log₆(108) = log₆(2² * 3³)

   Using the properties of logarithms, you can split this into two separate terms:

   log₆(2²) + log₆(3³)

   Now, apply the power rule of logarithms, which allows you to move exponents down as coefficients:

   2 * log₆(2) + 3 * log₆(3)

2. log₆(12⁻¹):

   This is equivalent to finding the logarithm of the reciprocal of 12, which is 1/12. So:

   log₆(12⁻¹) = log₆(1/12)

Now, you can combine the simplified expressions:

2 * log₆(2) + 3 * log₆(3) + log₆(1/12)

This is the simplified expression for "log₆(108) + log₆(12⁻¹)."