The opposite of exponentiation is the logarithm.
This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Given:

y = 6.72 ( $1.014^x$ ), where

y = population in billions
x = time in years

To find: Year when population is 8 billion, i.e., y = 8.

Finding:

8 = 6.72 ( $1.014^x$ )

=> $\frac{8}{6.72}= ( 1.014^x)$

Taking log on both sides

=> $log(\frac{8}{6.72})= log( 1.014^x)$

=> log(1.19) = x (log 1.014) (as $log_b(a)^m = m (log_b(a))$ )

=> $\frac{log(1.19)}{log (1.014)}$ = x

=> x = $\frac{0.0755}{0.006}$

=> x = 12.58

Hence, the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

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5 0

1 year ago

Find the zero of the function by rewriting the function in intercept form

Marat540 [252]

Given a quadratic function
y = 4x² - 19x - 5
or i will write it as
4x² - 19x - 5 = y

Zero of the function is when y have the value of zero.
So the quadratic equation will be
4x² - 19x - 5 = y
4x² - 19x - 5 = 0

Now make the equation to intercept form by factorization
4x² - 19x - 5 = 0
(4x + 1)(x - 5) = 0 (this is intercept form)

Solution 1
4x + 1 = 0
4x = -1
x = -1/4

Solution 2
x - 5 = 0
x = 5

SUMMARY
-1/4 and 5 are zero function of f(x) = 4x² - 19x - 5

4 0

4 years ago

How do I solve for x

Nataly [62]

28 divided by 2, which is 14.

4 0

3 years ago