Question
slove the equation
log2x+log x=7
log2x+log x=7
Answers
GPT 3.5
To solve the equation log2x + log x = 7, we can combine the logarithms using the logarithmic property: log(a) + log(b) = log(ab).
Therefore, we can rewrite the equation as: log(2x * x) = 7.
Simplifying further, we have log(2x^2) = 7.
Since log(2x^2) is the exponent to which the base 10 must be raised to obtain 2x^2, we can rewrite the equation in exponential form:
10^7 = 2x^2.
Now, we can solve this equation for x:
10^7 = 2x^2
Divide both sides of the equation by 2:
10^7 / 2 = x^2.
Taking the square root of both sides:
√(10^7 / 2) = x.
Calculating this value yields:
x ≈ 37416.62.
Therefore, the solution to the equation log2x + log x = 7 is x ≈ 37416.62.
Therefore, we can rewrite the equation as: log(2x * x) = 7.
Simplifying further, we have log(2x^2) = 7.
Since log(2x^2) is the exponent to which the base 10 must be raised to obtain 2x^2, we can rewrite the equation in exponential form:
10^7 = 2x^2.
Now, we can solve this equation for x:
10^7 = 2x^2
Divide both sides of the equation by 2:
10^7 / 2 = x^2.
Taking the square root of both sides:
√(10^7 / 2) = x.
Calculating this value yields:
x ≈ 37416.62.
Therefore, the solution to the equation log2x + log x = 7 is x ≈ 37416.62.