3 \log_{ 10 }({ 2x }) = 4
To solve the equation, we can start by using the property of logarithms that states:
n log_b(x) = log_b(x^n)
Therefore, we can rewrite the equation as:
log_{10}((2x)^3) = 4
Applying the power rule of logarithms, we can simplify further:
log_{10}(8x^3) = 4
Now, we can rewrite the equation in exponential form:
10^4 = 8x^3
Simplifying 10^4 gives us:
10000 = 8x^3
Dividing both sides of the equation by 8:
1250 = x^3
To find the value of x, we take the cube root of both sides:
x = ∛1250
Simplifying the cube root gives us:
x = 10∛5
Therefore, the solution for the equation is x = 10∛5.