Question

Logarithmi(c)/(e)xponential equatic log_(3)(5x+4)=log_(3)(10-3x)

Answer 1

To solve the equation log_3(5x+4) = log_3(10-3x), we can equate the expressions inside the logarithms and solve for x. The solution is x = 3/4.

Step-by-step explanation:

To solve the equation
`log3(5x+4) = log3(10-3x)` of logarithms that states if the logarithms of two numbers are equal, then the two numbers must be equal. So, we have 5x+4 = 10-3x.

Let's solve for x by simplifying the equation:

Adding 3x to both sides, we get 8x + 4 = 10. Subtracting 4 from both sides, we have 8x = 6. Dividing both sides by 8, we find that x = 3/4.