QuestionSolve for $x$ in the equation $\log _{4} 64=x$ . Choose from: {16, 3, 256, 68}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a logarithmic equation of the form $\log{b} a=x$ . . The base of the logarithm is4.
3. The number we are taking the logarithm of is64.

STEP 2

The equation we are trying to solve is $\log{4}64=x$ .

STEP 3

We can rewrite the logarithmic equation in exponential form. The base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and the number we are taking the logarithm of becomes the result of the exponentiation.
$^x =64$

STEP 4

Now we need to solve the equation $4^x =64$ for $x$ .

STEP 5

We can write64 as $4^3$ .
$4^x =4^3$

STEP 6

Since the bases are equal, the exponents must also be equal.
$x =3$ So, the solution to the equation $\log{4}64=x$ is $x =3$ .

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QuestionSolve for $x$ in the equation $\log _{4} 64=x$ . Choose from: {16, 3, 256, 68}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a logarithmic equation of the form $\log{b} a=x$ . . The base of the logarithm is4.
3. The number we are taking the logarithm of is64.

STEP 2

The equation we are trying to solve is $\log{4}64=x$ .

STEP 3

We can rewrite the logarithmic equation in exponential form. The base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and the number we are taking the logarithm of becomes the result of the exponentiation.
$^x =64$

STEP 4

Now we need to solve the equation $4^x =64$ for $x$ .

STEP 5

We can write64 as $4^3$ .
$4^x =4^3$

STEP 6

Since the bases are equal, the exponents must also be equal.
$x =3$ So, the solution to the equation $\log{4}64=x$ is $x =3$ .

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QuestionSolve for xxx in the equation log⁡464=x\log _{4} 64=xlog4​64=x. Choose from: {16, 3, 256, 68}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a logarithmic equation of the form log⁡ba=x\log{b} a=xlogba=x. . The base of the logarithm is4.3. The number we are taking the logarithm of is64.

STEP 2

The equation we are trying to solve is log⁡464=x\log{4}64=xlog464=x.

STEP 3

We can rewrite the logarithmic equation in exponential form. The base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and the number we are taking the logarithm of becomes the result of the exponentiation.x=64^x =64x=64

STEP 4

Now we need to solve the equation 4x=644^x =644x=64 for xxx.

STEP 5

We can write64 as 434^343.4x=434^x =4^34x=43

STEP 6

Since the bases are equal, the exponents must also be equal.x=3x =3x=3So, the solution to the equation log⁡464=x\log{4}64=xlog464=x is x=3x =3x=3.

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QuestionSolve for $x$ in the equation $\log _{4} 64=x$ . Choose from: {16, 3, 256, 68}.

Assumptions1. We are dealing with a logarithmic equation of the form $\log{b} a=x$ . . The base of the logarithm is4.
3. The number we are taking the logarithm of is64.

The equation we are trying to solve is $\log{4}64=x$ .

We can rewrite the logarithmic equation in exponential form. The base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and the number we are taking the logarithm of becomes the result of the exponentiation.
$^x =64$

Now we need to solve the equation $4^x =64$ for $x$ .

We can write64 as $4^3$ .
$4^x =4^3$

Since the bases are equal, the exponents must also be equal.
$x =3$ So, the solution to the equation $\log{4}64=x$ is $x =3$ .