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What is the value of xin the product of powers below? 6^9 * 6^x = 6^2 -11 -7 7 11

Sagot :

Given:

[tex]6^{9\text{ }}\ast6^x=6^2[/tex]

To find the value of x, first apply exponential property which is:

[tex]a^m\text{ }\ast a^{n\text{ }}=a^{m+n}[/tex]

Now we have:

[tex]6^{9+x\text{ }}=6^2[/tex]

Since both bases are equal, let's remove both bases, take the exponent and find x:

[tex]9\text{ + x = 2}[/tex]

Now subtract from both sides:

[tex]9\text{ - 9 + x = 2 - }9[/tex][tex]0\text{ + x }=\text{ -7}[/tex][tex]x\text{ = -7}[/tex]

The value of x is -7

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