Question

Please help I’m SOOO confused been trying to figure out for an hour and if u mind showing the work pls it’ll really help I’ll mark brainlist as well!

Answer 1

Answer: #2

Step-by-step explanation:

First things first, set both functions equal to each other. The purpose of this is to find the x value where both the functions will equal each other. So, we have:

$25^x^-^a=(\frac{1}{125} )^3^x^+^1$

There are two ways to do this. I'm going to choose the way which assumes you don't have a calculator. If we were to get the bases of the exponentials to be the same, we can simply set the exponents equal to each other. The fraction 1/125 is equal to 125^-1. Lets rewrite the equation:

$25^x^-^a=(125^-^1 )^3^x^+^1$

Using the rules of exponents, it allows us to multiply the -1 to the exponent to get:

$25^x^-^a=(125)^-^1^(^3^x^+^1^)$

$25^x^-^a=(125)^(^-^3^x^-^1^)$

The two numbers 25 and 125 can be represented as exponents with a base of 5. For example:

$5^2=25$

$5^3=125$

Plug these into the equation:

$(5^2)^x^-^a=(5^3)^(^-^3^x^-^1^)$

Do the same thing we did before, distribute the 2 and 3 into the exponents to get:

$(5)^2^(^x^-^a^)=(5)^3^(^-^3^x^-^1^)$

$(5)^2^x^-^2^a^=(5)^(^-^9^x^-^3^)$

Now that they have the exact same base, it means that the exponents absolutely must be equal to each other:

$2x-2a=-9x-3$

Add 9x to both sides, and add 2a to both sides to get:

$11x=-3+2a$

$11x=2a-3$

$x=(2a-3)/11$

The second way of doing this with a calculator would be to take the natural log of both sides. Logarithm rules states that the exponents can be brought to the front. So, you could have done:

$(x-a)ln(25)=(3x+1)ln(1/125)$

$x-a=(3x+1)\frac{ln(1/125)}{ln(25)}$

$x-a=(3x+1)(-1.5)$

$x-a=(3x+1)(-\frac{3}{2} )$

$2x-2a=-3(3x+1)$

$2x-2a=-9x-3$

$x=(2a-3)/11$