how do uu find the x int. , y int. , domain range asymtote of this equation
y=log to the base 10 (2x+3/x-5)
pleaseee need to understand before the test tmr!!!!
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To find the x-intercepts, we set y equal to zero and solve for x:
0 = log10(2x + 3)/(x - 5)
To eliminate the logarithm, we rewrite the equation in exponential form:
10^0 = 2x + 3/(x - 5)
10^0 simplifies to 1:
1 = 2x + 3/(x - 5)
We can then multiply both sides of the equation by (x - 5) to get rid of the fraction:
(x - 5) = 2x + 3
Expanding the equation:
x - 5 = 2x + 3
x - 2x = 3 + 5
-x = 8
Finally, we multiply both sides by -1 to solve for x:
x = -8
So, the x-intercept of the equation is x = -8.