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3 years ago

Evaluate the expression below when x = 24 and y = 6. sy

Mathematics

1 answer:

wlad13 [49]3 years ago

6 0

Do you mean xy instead of sy if so i’m pretty sure you would just multiply both of the numbers

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Given g(x)=-2x+2, solve for x when g(x)=8

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8^x=2<br> 8 to the power of x = 2. Find the value of x.

a_sh-v [17]

Answer:

$\huge{ \bold{ \boxed{ \sf{x = \frac{1}{3} }}}}$

☪ First , Let's know about Exponential Equation :

⤿ Let's take an equation : $\sf{ {2}^{x} = 8}$ .

In this equation , the variable ' x ' is the exponent of the base 2. Such an equation in which variable appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :

If $\sf{ {a}^{x} = {a}^{b} }$ , then $\sf{x = b}$
If $\sf{ {a}^{x} = 1}$ , then $\sf{ {a}^{x} = {a}^{0} }$ and x = 0

---------------------------------------------------------------

☯ Now , Let's Solve :

$\underline{ \sf{Given \: Exponential \: Equation \: : {8}^{x} = 2}}$

In this equation , the variable 'x' is the exponent of the base 8 .Write $\sf{ {8}^{x} }$ in exponential form with the base of 2

↦ $\sf{ {2}^{3x} = 2}$

Write the number 2 in exponential form with the base of 2.

↦ $\sf{ {2}^{3x} = {2}^{1}}$

Since the bases are same , cut 2 on both sides and set the exponents equal.

↦ $\sf{ { \cancel{2}} \: ^{3x} = { \cancel{2} } \: ^{1} }$

↦ $\sf{3x = 1}$

Divide both sides by 3

↦ $\sf{ \frac{3x}{3} = \frac{1}{3}}$

↦ $\boxed{ \bold{ \sf{x = \frac{1}{3} }}}$

And we're done!

Hope I helped!

Have a wonderful day! ツ

~TheAnimeGirl ♡

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3 years ago