Question

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

Answer 1

Given:

The logarithmic equation is:

`\log 970=x`

To find:

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

Solution:

Property of logarithm:

If
`\log_b a=x`, then
`a=b^x`

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

If
`\log a=x`, then
`a=10^x`

We have,

`\log 970=x`

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

`970=10^x`

Interchange the sides, we get

`10^x=970`

Therefore, the correct option is B, i.e.,
`10^x=970`.

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