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.