Question

Log x 7 + 2 log x 7 = 3

Answer 1

$log_{x}(7) + 2 log_{x}(7) = 3 \\ 3 log_{x}(7) = 3 \\ log_{x}(7) = 1 \\ 7 = {x}^{1} \\ x = 7$

Answer 2

log x 7 + 2 log x 7  = 3 log x 7 = 3

3 log x 7 = 3

log x 7 = 1

x = 7

Answer 3

To solve the equation log(x)7 + 2log(x)7 = 3, we can use the properties of logarithms to simplify the equation.

Recall the following properties of logarithms:

1. log_a(b) + log_a(c) = log_a(b * c)
2. log_a(b^n) = n * log_a(b)

Using these properties, we can rewrite the equation as follows:

log(x)7 + log(x^2)7 = 3

Applying property 1, we can combine the logarithms:

log(x)7 * (x^2)7 = 3

Now, we can rewrite the equation using property 2:

7log(x) + 14log(x) = 3

Combining the terms:

21log(x) = 3

Next, isolate the logarithm:

log(x) = 3/21

Simplifying the right side:

log(x) = 1/7

Now, we can rewrite the equation using the definition of logarithms:

x = 10^(1/7)

Therefore, the solution to the equation log(x)7 + 2log(x)7 = 3 is x = 10^(1/7).