Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Solve for x
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
- Load more...
Multiply both sides of the equation by $\log \left(3x-4\right)$
Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$
For two logarithms of the same base to be equal, their arguments must be equal. In other words, if $\log(a)=\log(b)$ then $a$ must equal $b$
Expand $\left(3x-4\right)^2$
The power of a product is equal to the product of it's factors raised to the same power
Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side
Subtract the values $16$ and $-16$
Combining like terms $-x^2$ and $-9x^2$
Factor the polynomial $-10x^2+24x$ by it's greatest common factor (GCF): $2x$
Divide both sides of the equation by $2$
Break the equation in $2$ factors and set each equal to zero, to obtain
Solve the equation ($1$)
The variable is already isolated, so the solution is
Solve the equation ($2$)
We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $12$ from both sides of the equation
Canceling terms on both sides
Divide both sides of the equation by $-5$
Simplify the fraction $\frac{-12}{-5}$
Combining all solutions, the $2$ solutions of the equation are
Verify that the solutions obtained are valid in the initial equation
The valid solutions to the logarithmic equation are the ones that, when replaced in the original equation, don't result in any logarithm of negative numbers or zero, since in those cases the logarithm does not exist
