Question

What is the solution to log7(x – 4) = log7(4x 5) ? x = –3 x = –2 x = –1 x = 0 There is no solution.

Answer 1

You can use the definition of logarithm to evaluate x and get the solution of the given equation.

The solution to the given equation is given by: Option A: x= -3

What is the definition of logarithm?

If a raised to power b equates to c, then we can say that logarithm of c with base a is b.

Or symbolically:

$a^b = c \implies b = log_a(c)$

How to use definition of logarithm to solve the given equation?

We can reverse the definition of log to get back to representation in powers.

Thus,

$log_7(x-4) = log_7(4x + 5)\\\\ x-4 = 7^{log_7(4x+5)}\\\\ x-4 = 4x + 5\\ 3x = -9\\ x = -\dfrac{9}{3} = -3$

I  used the fact that  

 $log_a(b) = log_a(b)\\\\ b = a^{log_a(b)}$

Thus, the solution of given equation is given by Option A: x = -3

Learn more about logarithm here:

https://brainly.com/question/14247920

Answer 2

Answer:

There is no solution

Step-by-step explanation: