Which of the following exponential equations is equivalent to the logarithmic equation below?
log 970 = x
A. x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X

Given:

The logarithmic equation is:

To find:

The exponential equations that is equivalent to the given logarithmic equation.

Solution:

Property of logarithm:

If , then

We know that the base log is always 10 if it is not mentioned.

If , then

We have,

Here, base is 10 and the value of a is 970. By using the properties of exponents, we get

Interchange the sides, we get

Therefore, the correct option is B, i.e., .

Note: It should be "=" instead of "-" in option B.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2