QuestionFind the value of $b$ if the graph of $y=\log _{b} x$ passes through $(8, 2)$ . Choices: a. 10, b. 2, c. $2\sqrt{2}$ , d. $2\sqrt{3}$ .

Studdy Solution

STEP 1

Assumptions1. The equation of the graph is $y=\log{b} x$ . The graph passes through the point $(8 ;)$ 3. We need to find the value of $b$

STEP 2

The logarithm equation $y=\log{b} x$ can be rewritten in exponential form as $b^y = x$ .

STEP 3

Substitute the coordinates of the point $(8 ;2)$ into the exponential form of the equation.
$b^2 =8$

STEP 4

To solve for $b$ , we need to take the square root of both sides of the equation.
$b = \sqrt{8}$

STEP 5

implify the square root of8.
$b =2 \sqrt{2}$ So, the value of $b$ is $2 \sqrt{2}$ .

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QuestionFind the value of $b$ if the graph of $y=\log _{b} x$ passes through $(8, 2)$ . Choices: a. 10, b. 2, c. $2\sqrt{2}$ , d. $2\sqrt{3}$ .

Studdy Solution

STEP 1

Assumptions1. The equation of the graph is $y=\log{b} x$ . The graph passes through the point $(8 ;)$ 3. We need to find the value of $b$

STEP 2

The logarithm equation $y=\log{b} x$ can be rewritten in exponential form as $b^y = x$ .

STEP 3

Substitute the coordinates of the point $(8 ;2)$ into the exponential form of the equation.
$b^2 =8$

STEP 4

To solve for $b$ , we need to take the square root of both sides of the equation.
$b = \sqrt{8}$

STEP 5

implify the square root of8.
$b =2 \sqrt{2}$ So, the value of $b$ is $2 \sqrt{2}$ .

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QuestionFind the value of bbb if the graph of y=log⁡bxy=\log _{b} xy=logb​x passes through (8,2)(8, 2)(8,2). Choices: a. 10, b. 2, c. 222\sqrt{2}22​, d. 232\sqrt{3}23​.

Studdy Solution

STEP 1

Assumptions1. The equation of the graph is y=log⁡bxy=\log{b} xy=logbx . The graph passes through the point (8;)(8 ;)(8;)3. We need to find the value of bbb

STEP 2

The logarithm equation y=log⁡bxy=\log{b} xy=logbx can be rewritten in exponential form as by=xb^y = xby=x.

STEP 3

Substitute the coordinates of the point (8;2)(8 ;2)(8;2) into the exponential form of the equation.b2=8b^2 =8b2=8

STEP 4

To solve for bbb, we need to take the square root of both sides of the equation.b=8b = \sqrt{8}b=8​

STEP 5

implify the square root of8.b=22b =2 \sqrt{2}b=22​So, the value of bbb is 222 \sqrt{2}22​.

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QuestionFind the value of $b$ if the graph of $y=\log _{b} x$ passes through $(8, 2)$ . Choices: a. 10, b. 2, c. $2\sqrt{2}$ , d. $2\sqrt{3}$ .

Assumptions1. The equation of the graph is $y=\log{b} x$ . The graph passes through the point $(8 ;)$ 3. We need to find the value of $b$

The logarithm equation $y=\log{b} x$ can be rewritten in exponential form as $b^y = x$ .

Substitute the coordinates of the point $(8 ;2)$ into the exponential form of the equation.
$b^2 =8$

To solve for $b$ , we need to take the square root of both sides of the equation.
$b = \sqrt{8}$

implify the square root of8.
$b =2 \sqrt{2}$ So, the value of $b$ is $2 \sqrt{2}$ .