# Find x if 3log5+logx²=log1/125

## using the rules of logs, you have

log(5^3 * x^2) = log(1/125)

125x^2 = 1/125

x^2 = 1/(125^2) = 5^-6

x = ±5^-3 = ±1/125

## To find the value of x, we need to solve the equation:

3log5 + log(x²) = log(1/125)

First, let's simplify further using logarithmic properties.

Remember that log(a) + log(b) = log(a * b).

Using this property, we can rewrite the equation as:

log(5^3) + log(x²) = log(1/125)

Next, apply another property of logarithms: log(a^b) = b * log(a).

Now we have:

log(125) + log(x²) = log(1/125)

Since we have log on both sides of the equation, we can eliminate them:

125 * x² = 1/125

Now, we can simplify further by multiplying both sides of the equation by 125:

125 * 125 * x² = 1

Simplifying:

(125^2) * x² = 1

Now, divide both sides of the equation by (125^2) to isolate x²:

x² = 1 / (125^2)

Finally, take the square root of both sides to solve for x:

x = ± √(1 / (125^2))

The value of x is equal to ±1/125.

## To solve this equation for x, we need to use logarithmic properties and algebraic manipulation.

First, let's apply the logarithmic property:

3log5 + logx² = log1/125

We can simplify the equation further by using the logarithmic property, log(a^b) = b*log(a):

log5^3 + logx² = log1/125

Now, use the property log(a) + log(b) = log(a*b):

log(5^3 * x²) = log1/125

Since we have the same logarithm on both sides of the equation, we can eliminate the logarithm:

5^3 * x² = 1/125

Simplify each side:

125x² = 1/125

Multiply both sides by 125 to get rid of the fraction:

125 * 125x² = 1

15625x² = 1

To solve for x², divide both sides by 15625:

x² = 1 / 15625

Take the square root of both sides to find x:

x = sqrt(1 / 15625)

Now we can simplify further:

x = 1 / sqrt(15625)

Since 15625 is a perfect square (125^2), we can simplify it:

x = 1 / 125

Therefore, x = 1/125.