Question Rearrange the steps to solve $5^{(6 x-9)}=125$ .

Studdy Solution

STEP 1

Assumptions
1. The equation given is $5^{(6x-9)} = 125$ .
2. We are to solve for $x$ .
3. We need to manipulate the equation using properties of exponents and basic algebraic operations.
4. The base of the exponent on the left side is 5, and we will need to express 125 as a power of 5 to solve the equation.
5. We will not need to use all the provided operations (subtract 9 from each side, add 9 to each side, divide each side by 5, divide each side by 6).

STEP 2

First, we recognize that 125 is a power of 5. We need to rewrite 125 as a power of 5 to be able to equate the exponents.
$125 = 5^3$

STEP 3

Now, we replace 125 in the original equation with $5^3$ .
$5^{(6x-9)} = 5^3$

STEP 4

Since the bases are the same and the equation is an equality, we can equate the exponents.
$6x - 9 = 3$

STEP 5

Now, we solve for $x$ by first adding 9 to each side of the equation.
$6x - 9 + 9 = 3 + 9$

STEP 6

Simplify the equation.
$6x = 12$

STEP 7

Finally, we divide each side by 6 to solve for $x$ .
$\frac{6x}{6} = \frac{12}{6}$

STEP 8

Calculate the value of $x$ .
$x = 2$
The correct sequence of explanations to solve the given equation is:
1. Rewrite 125 as a power of 5
2. Equate the exponents of the equation
3. Add 9 to each side
4. Divide each side by 6

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Question Rearrange the steps to solve $5^{(6 x-9)}=125$ .

Studdy Solution

STEP 1

STEP 2

First, we recognize that 125 is a power of 5. We need to rewrite 125 as a power of 5 to be able to equate the exponents.
$125 = 5^3$

STEP 3

Now, we replace 125 in the original equation with $5^3$ .
$5^{(6x-9)} = 5^3$

STEP 4

Since the bases are the same and the equation is an equality, we can equate the exponents.
$6x - 9 = 3$

STEP 5

Now, we solve for $x$ by first adding 9 to each side of the equation.
$6x - 9 + 9 = 3 + 9$

STEP 6

Simplify the equation.
$6x = 12$

STEP 7

Finally, we divide each side by 6 to solve for $x$ .
$\frac{6x}{6} = \frac{12}{6}$

STEP 8

Calculate the value of $x$ .
$x = 2$
The correct sequence of explanations to solve the given equation is:
1. Rewrite 125 as a power of 5
2. Equate the exponents of the equation
3. Add 9 to each side
4. Divide each side by 6

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Question Rearrange the steps to solve 5(6x−9)=1255^{(6 x-9)}=1255(6x−9)=125.

Studdy Solution

STEP 1

STEP 2

First, we recognize that 125 is a power of 5. We need to rewrite 125 as a power of 5 to be able to equate the exponents.125=53125 = 5^3125=53

STEP 3

Now, we replace 125 in the original equation with 535^353.5(6x−9)=535^{(6x-9)} = 5^35(6x−9)=53

STEP 4

Since the bases are the same and the equation is an equality, we can equate the exponents.6x−9=36x - 9 = 36x−9=3

STEP 5

Now, we solve for xxx by first adding 9 to each side of the equation.6x−9+9=3+96x - 9 + 9 = 3 + 96x−9+9=3+9

STEP 6

Simplify the equation.6x=126x = 126x=12

STEP 7

Finally, we divide each side by 6 to solve for xxx.6x6=126\frac{6x}{6} = \frac{12}{6}66x​=612​

STEP 8

Calculate the value of xxx.x=2x = 2x=2The correct sequence of explanations to solve the given equation is:1. Rewrite 125 as a power of 52. Equate the exponents of the equation3. Add 9 to each side4. Divide each side by 6

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Question Rearrange the steps to solve $5^{(6 x-9)}=125$ .

First, we recognize that 125 is a power of 5. We need to rewrite 125 as a power of 5 to be able to equate the exponents.
$125 = 5^3$

Now, we replace 125 in the original equation with $5^3$ .
$5^{(6x-9)} = 5^3$

Since the bases are the same and the equation is an equality, we can equate the exponents.
$6x - 9 = 3$

Now, we solve for $x$ by first adding 9 to each side of the equation.
$6x - 9 + 9 = 3 + 9$

Simplify the equation.
$6x = 12$

Finally, we divide each side by 6 to solve for $x$ .
$\frac{6x}{6} = \frac{12}{6}$

Calculate the value of $x$ .
$x = 2$
The correct sequence of explanations to solve the given equation is:
1. Rewrite 125 as a power of 5
2. Equate the exponents of the equation
3. Add 9 to each side
4. Divide each side by 6