QuestionRewrite the expression $3^{-3}$ using a logarithm.

Studdy Solution

STEP 1

Assumptions1. The base of the exponential expression is3. . The exponent of the exponential expression is -3.
3. The result of the exponential expression is $\frac{1}{27}$ .
4. The base of the logarithm will be the same as the base of the exponential expression, which is3.

STEP 2

The general form of an exponential expression is $b^x = y$ , where $b$ is the base, $x$ is the exponent, and $y$ is the result.
In this case, $b =$ , $x = -$ , and $y = \frac{1}{27}$ .

STEP 3

The general form of a logarithmic expression is $\log_b y = x$ , where $b$ is the base, $y$ is the result, and $x$ is the exponent.
We want to convert the exponential expression into this logarithmic form.

STEP 4

Substitute the values of $b$ , $x$ , and $y$ from the exponential expression into the logarithmic form.
$\log_b y = x$ becomes $\log3 \frac{1}{27} = -3$

STEP 5

This is the equivalent logarithmic expression for the given exponential expression. Therefore, the solution is $\log3 \frac{1}{27} = -3$

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QuestionRewrite the expression $3^{-3}$ using a logarithm.

Studdy Solution

STEP 1

Assumptions1. The base of the exponential expression is3. . The exponent of the exponential expression is -3.
3. The result of the exponential expression is $\frac{1}{27}$ .
4. The base of the logarithm will be the same as the base of the exponential expression, which is3.

STEP 2

The general form of an exponential expression is $b^x = y$ , where $b$ is the base, $x$ is the exponent, and $y$ is the result.
In this case, $b =$ , $x = -$ , and $y = \frac{1}{27}$ .

STEP 3

The general form of a logarithmic expression is $\log_b y = x$ , where $b$ is the base, $y$ is the result, and $x$ is the exponent.
We want to convert the exponential expression into this logarithmic form.

STEP 4

Substitute the values of $b$ , $x$ , and $y$ from the exponential expression into the logarithmic form.
$\log_b y = x$ becomes $\log3 \frac{1}{27} = -3$

STEP 5

This is the equivalent logarithmic expression for the given exponential expression. Therefore, the solution is $\log3 \frac{1}{27} = -3$

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QuestionRewrite the expression 3−33^{-3}3−3 using a logarithm.

Studdy Solution

STEP 1

Assumptions1. The base of the exponential expression is3. . The exponent of the exponential expression is -3.3. The result of the exponential expression is 127\frac{1}{27}271​.4. The base of the logarithm will be the same as the base of the exponential expression, which is3.

STEP 2

The general form of an exponential expression is bx=yb^x = ybx=y, where bbb is the base, xxx is the exponent, and yyy is the result.In this case, b=b =b=, x=−x = -x=−, and y=127y = \frac{1}{27}y=271​.

STEP 3

The general form of a logarithmic expression is log⁡by=x\log_b y = xlogb​y=x, where bbb is the base, yyy is the result, and xxx is the exponent.We want to convert the exponential expression into this logarithmic form.

STEP 4

Substitute the values of bbb, xxx, and yyy from the exponential expression into the logarithmic form.log⁡by=x\log_b y = xlogb​y=xbecomeslog⁡3127=−3\log3 \frac{1}{27} = -3log3271​=−3

STEP 5

This is the equivalent logarithmic expression for the given exponential expression. Therefore, the solution islog⁡3127=−3\log3 \frac{1}{27} = -3log3271​=−3

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QuestionRewrite the expression $3^{-3}$ using a logarithm.

Assumptions1. The base of the exponential expression is3. . The exponent of the exponential expression is -3.
3. The result of the exponential expression is $\frac{1}{27}$ .
4. The base of the logarithm will be the same as the base of the exponential expression, which is3.

The general form of an exponential expression is $b^x = y$ , where $b$ is the base, $x$ is the exponent, and $y$ is the result.
In this case, $b =$ , $x = -$ , and $y = \frac{1}{27}$ .

The general form of a logarithmic expression is $\log_b y = x$ , where $b$ is the base, $y$ is the result, and $x$ is the exponent.
We want to convert the exponential expression into this logarithmic form.

Substitute the values of $b$ , $x$ , and $y$ from the exponential expression into the logarithmic form.
$\log_b y = x$ becomes $\log3 \frac{1}{27} = -3$

This is the equivalent logarithmic expression for the given exponential expression. Therefore, the solution is $\log3 \frac{1}{27} = -3$