4 log x + 5 log x - 7 log x = log 16?
(X^4) * (X^5) /(X^7) = 16
X^4+5/ X^7 = 16
X^9 ÷ X^7 =16
X^9-7 = 16
X^2= 16
√X^2 = √16
X= 4
(x^4) * (x^5) / (x^7) = 16
logs are undefined for negative quantities
To solve the given equation, we can combine the logarithms using the properties of logarithms.
First, let's simplify the left side of the equation. Since we have three terms with the same base (log x), we can combine them using the addition property of logarithms:
4 log x + 5 log x - 7 log x = (4 + 5 - 7) log x = 2 log x
Now, the equation becomes:
2 log x = log 16
To solve for x, we need to get rid of the logarithm. We can do this by applying the exponential function to both sides of the equation. Since the base of the logarithm is 10 (assuming it's not mentioned), we can rewrite the equation as:
x^2 = 16
Taking the square root of both sides, we have:
x = ±√16
Simplifying further:
x = ±4
Therefore, the solutions to the equation are x = 4 and x = -4.
To solve the equation 4 log x + 5 log x - 7 log x = log 16, we can combine the logarithms on the left-hand side using the properties of logarithms.
First, let's apply the power rule of logarithms, which states that log a^b = b * log a. Using this rule, we can rewrite the equation as:
log x^4 + log x^5 - log x^7 = log 16
Next, we can apply the product rule of logarithms, which states that log a + log b = log(ab). Using this rule, we can further simplify the equation as:
log (x^4 * x^5) - log x^7 = log 16
Simplifying the expression inside the logarithm using the property x^a * x^b = x^(a+b), we get:
log x^9 - log x^7 = log 16
Now, let's combine the logarithms on the left side of the equation using the quotient rule of logarithms, which states that log a - log b = log(a/b). Applying this rule, we have:
log (x^9 / x^7) = log 16
Simplifying the expression inside the logarithm using the property x^a / x^b = x^(a-b), we get:
log (x^2) = log 16
Since the logarithms on both sides of the equation have the same base (base 10 in this case), we can drop the logarithm and equate the expressions inside:
x^2 = 16
Taking the square root of both sides, we have:
x = ± √16
Therefore, the solutions to the equation are x = ±4.