Question

Log(x,81)+log(x,9)+log(x, 3)=7

Answer 1

$log_{x}81 + log_{x}9 + log_{x}3 = 7 \\ log_{x}(81 \times 9 \times 3) = 7 \\ log_{x}( {3}^{4} \times {3}^{2} \times 3) = 7 \\ log_{x} {3}^{7} = 7 \\ 7 log_{x}3 = 7 \\ log_{x}3 = 1 \\ x = 3$

Answer 2

To solve the equation log(x, 81) + log(x, 9) + log(x, 3) = 7, you can use logarithmic properties to simplify it and then solve for x.

First, recall the logarithmic property that allows you to combine logarithms with the same base when adding:

log_b(a) + log_b(c) = log_b(a * c)

Apply this property to your equation:

log(x, 81) + log(x, 9) + log(x, 3) = log(x, 81 * 9 * 3)

Now, simplify the right side:

log(x, 81 * 9 * 3) = log(x, 2187)

Now, we have:

log(x, 2187) = 7

To solve for x, you can use the definition of a logarithm:

log_b(a) = c is equivalent to b^c = a

In this case, you have:

x^7 = 2187

Now, you can solve for x by taking the seventh root of both sides:

x = 2187^(1/7)

Calculating the seventh root of 2187:

x ≈ 3.0

So, the approximate value of x that satisfies the equation is x ≈ 3.0.