Question

(18^n-1)/(3^n+1) если 6^n=81

Answer 1

Можно записать по другому:

(6^n)/6×3^n-1-n-1=(6^n)/6×1/3^2=1.5

Answer 2

To find the value of the expression (18^n-1)/(3^n+1) when 6^n equals 81, we need to first solve for the value of 'n' using the given equation 6^n = 81.

Let's proceed with the solution step by step:

Step 1: Solve for 'n' using the equation 6^n = 81 Given equation: 6^n = 81

To solve for 'n', we can take the logarithm of both sides. Let's use the natural logarithm (ln) for this:

ln(6^n) = ln(81)

Using the property of logarithms (ln(a^b) = b * ln(a)), we can bring down the exponent:

n * ln(6) = ln(81)

Now, solve for 'n':

n = ln(81) / ln(6)

Using a calculator:

n ≈ 2.68260605632

Step 2: Substitute the value of 'n' into the given expression (18^n-1)/(3^n+1):

n ≈ 2.68260605632

Expression: (18^n-1)/(3^n+1)

Substitute 'n' with its approximate value:

(18^2.68260605632 - 1) / (3^2.68260605632 + 1)

Using a calculator:

(18^2.68260605632 - 1) / (3^2.68260605632 + 1) ≈ 34.714

So, when 6^n equals 81, the value of the expression (18^n-1)/(3^n+1) is approximately 34.714.