Question

Is f(x)=3x5^2x-3 an exponential function? If so, write it in the form f(x)=ab^x

Answer 1

Answer:

$f(x)=\frac{3}{125} * 25^x$

Step-by-step explanation:

Given

$f(x)=3*5^{2x-3}$

Required

To determine if it is an exponential function, we have to write in form of

$f(x) = ab^x$

If we're able to do so, then the function is an exponential function.

If otherwise, then it is not

$f(x)=3*5^{2x-3}$

Apply Law of indices

$f(x)=3*\frac{5^{2x}}{5^3}$

Express 5^3 as 125

$f(x)=3*\frac{5^{2x}}{125}$

Factorize the exponent of 5

$f(x)=3*\frac{5^{(2)x}}{125}$

Express 5^2 as 25

$f(x)=3*\frac{25^x}{125}$

This can be rewritten as:

$f(x)=\frac{3}{125} * 25^x$

By comparing the above to $f(x) = ab^x$

We have that

$a = \frac{3}{125}$

$b^x = 25^x$

Since, we've be able to express the function as $f(x) = ab^x$

Then, $f(x)=3*5^{2x-3}$ is an exponential function

Answer 2

The expression in exponential form is expressed as $g(x)=\frac{3}{125} \cdot 25^x$. Option C is correct.

Given the equation $f(x) = 3\cdot 5^{2x-3}$, we are to write in the form $a(b)^x$

Simplifying the given expression, we will have:

$g(x) = 3\cdot 5^{2x-3}\\g(x) = 3\cdot 5^{2x} \cdot 5^{-3}\\g(x) =\frac{3}{5^3}\cdot (5^2)^x\\g(x)=\frac{3}{125} \cdot 25^x$

Hence the expression in exponential form is expressed as $g(x)=\frac{3}{125} \cdot 25^x$

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