comparable expressionsGive examples about exponential equations solved without logarithms. I've put 2^x=16 and I'm not sure if I'm right because I don't have exponent to 16.

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The alternative method to solve the exponential equation is to form matching bases both sides such that:

Notice that when you have matching bases, you only need to equate the exponents.

 

 

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We have 2^x = 16

To solve, first e will rewrite the numbers so the bases are equal.

We will factor 16.

==> 16 = 4*4 = 2*2*2*2 = 2^4

Now we will substitute into the equation.

==> 2^x = 2^4

Now we notice that the bases are equal, then the exponents must be equal too.

Then, we conclude that x = 4.

To check, we will substitute with x=4.

==> 2^x = 16

==> 2^4 = 16

==> 16 =16

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know that for solving exponential equations without the help of logarithms, we must have comparable bases both sides of the equal sign.

The assumption you've made is right, because 16 is a power of 2.

So, you have to write 16 as a power of 2, in order to get comparable bases.

2^x = 2^4

The exponential are equals if only the exponents are equals.

x = 4

You also could have:

3^(2x - 1) = 3^x

2x - 1 = x

x - 1 = 0

x = 1

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