Question

Log5 x=2log5 3+1/3log5 8

Answer 1

Log5 x=log5 9+log5 2
log5 x=log5 18
x=18

Answer 2

To solve the equation log5(x) = 2log5(3) + (1/3)log5(8), we'll use logarithmic properties to simplify it step by step.

1. Recall the following logarithmic properties: a) log(a) + log(b) = log(ab) b) log(a) - log(b) = log(a/b) c) n*log(a) = log(a^n), where n is any constant

2. Apply the properties to the given equation:

log5(x) = 2log5(3) + (1/3)log5(8)

Using property (1): log5(x) = log5(3^2) + log5(8^(1/3))

Using property (c): log5(x) = log5(9) + log5(2)

3. Simplify the expression further:

Since log5(9) means "the power to which 5 must be raised to get 9," and log5(2) means "the power to which 5 must be raised to get 2," we have:

log5(x) = log5(9 * 2)

4. Continue simplifying:

log5(x) = log5(18)

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

x = 18

So, the solution to the equation is x = 18.