I guess the original expression is 125 = 5^x
If you apply logarithms to both sides, you get:
log (125) = x * log (5) <----------- logaritmic equation
=> x = log (125) / log(5)
Given that 125 is 5^3
you can simplify to
x = log (5^3) / log(5) = 3 log (5) / log (5) = 3 * 1 = 3
There you have the expression as a logarithmic equation and the solution of the equation.
Because you are shifting the function to the left by 2 units, you will represent that as:
Because you are shifting the function to the left by 2 units, you will represent that as:

Generally, if you are moving to the left, it's seen going in the negative direction, but remember since f(x) is going to the left, it means that you are solving for x. So, solve for x in (x + 2), you get x = -2. Hopefully this makes sense.
The, you are dilating the entire function in which you have to multiply the
entire thing. Let's do it:

Which is equal to:

So, your answer is D. If anything doesn't make sense to you, please tell me, I'd be happy to explain!
Answer:
B
Step-by-step explanation:
First label the equations.
6x +3y= 18 -----(1)
y= -2x +5 -----(2)
subst. (2) into (1):
6x +3(-2x +5)= 18
6x +3(-2x) +3(5)= 18 (expand)
6x -6x +15= 18
15= 18 (simplify)
(reject)
There is no solution.
<u>Further explanation</u><u>:</u>
If I rewrite the first equation into the form of y=mx+c, I would get
6x +3y=18
3y= 18 -6x (bring y term to one side)
y= 6- 2x (÷3 throughout)
y= -2x +6
Notice that the gradients of both lines are equal ( -2). This implies that they are parallel to each other and will never meet. Hence there are no solutions.
If you are moving the decimal point to the left, the exponent is negative. If you move it to the right, the exponent is positive.
There is only one negative exponent here, and it is the first option.
So:
A number is being written in scientific notation. The student moves the decimal point to the left 3 places and A<span>. multiplies by 10^-3.</span>
<span>239.63 ÷ 7.51
estimate
= 240 / 8
= 30</span>