What is X?
log(base 5)x^10-log(base5)x^6=21
log5 x^4 = 21 (subtract logs is divide)
4 log5 x = 21
log5 x = 21/4
x = 5^(21/4)
thank you!
Log58x3
To find the value of x in the equation log(base 5)x^10 - log(base 5)x^6 = 21, we can use the properties of logarithms.
First, we need to simplify the equation using the quotient rule of logarithms. According to the quotient rule, log(a) - log(b) = log(a/b).
Applying the quotient rule in our equation, we get log(base 5) (x^10 / x^6) = 21.
Now, we need to simplify the expression inside the logarithm. When dividing the same base raised to different exponents, we can subtract the exponents. In this case, x^10 / x^6 = x^(10-6) = x^4.
Therefore, our equation becomes log(base 5) x^4 = 21.
To get rid of the logarithm, we can rewrite the equation in exponential form. For any logarithm with base b and exponent y, it can be rewritten as b^y.
In this case, we have 5^21 = x^4. Evaluating 5^21 on a calculator, we get approximately 7,625,597,484,987,545.
So, x^4 = 7,625,597,484,987,545.
Finally, to solve for x, we can take the fourth root of both sides of the equation. Taking the fourth root of 7,625,597,484,987,545 gives us approximately 103.
Hence, x ≈ 103.