asked 39.5k views
3 votes
Solve the following logarithmic simultaneous equations:

logₓ y = 2
y log₄ 4 = x log₈ 8

1 Answer

2 votes

Final answer:

The given logarithmic equations are not presented in a clear and usable form. Typically, logarithmic equations are solved by converting to exponential form and using properties of logarithms such as the power, product, and quotient properties.

Step-by-step explanation:

To solve the given logarithmic simultaneous equations, we must first clarify the actual equations since the statement given seems to reference constants and variables without the necessary context. The general approach for solving logarithmic equations involves converting the logarithms into exponential form and utilizing the properties of exponents to find the variables.

One property of logarithms that is often used is that the logarithm of a power, such as loga(bn), is equal to n · loga(b). Also, the basic property that loga(a) equals 1 is utilized. Furthermore, the product and quotient properties of logarithms may also be applied, where loga(xy) = loga(x) + loga(y) and loga(x/y) = loga(x) - loga(y).

It's also worth noting that converting a logarithmic equation to exponential form often simplifies the process of finding a solution. For instance, the equation logb(x) = y can be rewritten as by = x.

answered
User Inspirednz
by
8.2k points
Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.