Question

Lg 3 x- lg 9 x+ lg 81 x = 3/4

Answer 1

$lg3x-lg9x+lg81x=3/4$
$lg((3x/9x)*81x)=3/4$
$lg27x=3/4$
$10^{3/4}=27x$
$x=10^{3/4}/27$

Answer 2

To solve the equation LG(3x) - LG(9x) + LG(81x) = 3/4, we can use the properties of logarithms to simplify the expression.

First, let's recall the logarithmic properties:

1. LG(a) - LG(b) = LG(a/b)
2. LG(a) + LG(b) = LG(a * b)
3. LG(a^b) = b * LG(a)

Now, let's simplify the equation step by step:

LG(3x) - LG(9x) + LG(81x) = 3/4

Using property 1, we can combine the first two logarithms:

LG((3x)/(9x)) + LG(81x) = 3/4

Simplifying inside the first logarithm:

LG(1/3) + LG(81x) = 3/4

Using property 3, we can rewrite the first logarithm:

(-1) * LG(3) + LG(81x) = 3/4

Next, let's simplify the second logarithm:

(-1) * LG(3) + LG(3^4 * x) = 3/4

Using property 3 again:

(-1) * LG(3) + 4 * LG(3) + LG(x) = 3/4

Combining like terms:

3 * LG(3) + LG(x) = 3/4

Now, let's isolate the LG(x) term by moving the 3 * LG(3) term to the other side:

LG(x) = 3/4 - 3 * LG(3)

Now, we can evaluate the right-hand side of the equation using the given values or a calculator:

LG(x) = 3/4 - 3 * LG(3)

LG(x) ≈ 3/4 - 3 * 0.477 = 0.75 - 1.431 ≈ -0.681

Finally, to solve for x, we need to convert the logarithmic equation into an exponential equation:

x = 10^(LG(x))

Substituting the approximate value of LG(x) into the equation:

x ≈ 10^(-0.681)

Using a calculator, we find:

x ≈ 0.207

Therefore, the approximate solution to the equation LG(3x) - LG(9x) + LG(81x) = 3/4 is x ≈ 0.207.