QuestionSolve for $x$ in the equation $3 m^{x+1} = 18$ .

Studdy Solution

STEP 1

Assumptions1. The equation to solve is $3 m^{x+1}=18$ . The base of the exponent, m, is a positive real number3. The exponent, x, is the variable we need to solve for

STEP 2

First, we need to isolate the term with the exponent on one side of the equation. We can do this by dividing both sides of the equation by.
$\frac{ m^{x+1}}{} = \frac{18}{}$

STEP 3

implify the equation.
$m^{x+1} =6$

STEP 4

To solve for x, we need to remove the exponent. We can do this by taking the logarithm of both sides of the equation. We'll use the natural logarithm (ln) for this.
$ln(m^{x+1}) = ln(6)$

STEP 5

Using the property of logarithms that allows us to bring the exponent down as a multiplier, we rewrite the left side of the equation.
$(x+1) \cdot ln(m) = ln()$

STEP 6

Now, we isolate x by subtracting1 from both sides of the equation.
$x \cdot ln(m) = ln(6) - ln(m)$

STEP 7

Finally, we can solve for x by dividing both sides of the equation by ln(m).
$x = \frac{ln(6) - ln(m)}{ln(m)}$ This is the solution for x in terms of m.

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QuestionSolve for $x$ in the equation $3 m^{x+1} = 18$ .

Studdy Solution

STEP 1

Assumptions1. The equation to solve is $3 m^{x+1}=18$ . The base of the exponent, m, is a positive real number3. The exponent, x, is the variable we need to solve for

STEP 2

First, we need to isolate the term with the exponent on one side of the equation. We can do this by dividing both sides of the equation by.
$\frac{ m^{x+1}}{} = \frac{18}{}$

STEP 3

implify the equation.
$m^{x+1} =6$

STEP 4

To solve for x, we need to remove the exponent. We can do this by taking the logarithm of both sides of the equation. We'll use the natural logarithm (ln) for this.
$ln(m^{x+1}) = ln(6)$

STEP 5

Using the property of logarithms that allows us to bring the exponent down as a multiplier, we rewrite the left side of the equation.
$(x+1) \cdot ln(m) = ln()$

STEP 6

Now, we isolate x by subtracting1 from both sides of the equation.
$x \cdot ln(m) = ln(6) - ln(m)$

STEP 7

Finally, we can solve for x by dividing both sides of the equation by ln(m).
$x = \frac{ln(6) - ln(m)}{ln(m)}$ This is the solution for x in terms of m.

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QuestionSolve for xxx in the equation 3mx+1=183 m^{x+1} = 183mx+1=18.

Studdy Solution

STEP 1

Assumptions1. The equation to solve is 3mx+1=183 m^{x+1}=183mx+1=18 . The base of the exponent, m, is a positive real number3. The exponent, x, is the variable we need to solve for

STEP 2

First, we need to isolate the term with the exponent on one side of the equation. We can do this by dividing both sides of the equation by.mx+1=18\frac{ m^{x+1}}{} = \frac{18}{}mx+1​=18​

STEP 3

implify the equation.mx+1=6m^{x+1} =6mx+1=6

STEP 4

To solve for x, we need to remove the exponent. We can do this by taking the logarithm of both sides of the equation. We'll use the natural logarithm (ln) for this.ln(mx+1)=ln(6)ln(m^{x+1}) = ln(6)ln(mx+1)=ln(6)

STEP 5

Using the property of logarithms that allows us to bring the exponent down as a multiplier, we rewrite the left side of the equation.(x+1)⋅ln(m)=ln() (x+1) \cdot ln(m) = ln()(x+1)⋅ln(m)=ln()

STEP 6

Now, we isolate x by subtracting1 from both sides of the equation.x⋅ln(m)=ln(6)−ln(m) x \cdot ln(m) = ln(6) - ln(m)x⋅ln(m)=ln(6)−ln(m)

STEP 7

Finally, we can solve for x by dividing both sides of the equation by ln(m).x=ln(6)−ln(m)ln(m) x = \frac{ln(6) - ln(m)}{ln(m)}x=ln(m)ln(6)−ln(m)​This is the solution for x in terms of m.

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QuestionSolve for $x$ in the equation $3 m^{x+1} = 18$ .

Assumptions1. The equation to solve is $3 m^{x+1}=18$ . The base of the exponent, m, is a positive real number3. The exponent, x, is the variable we need to solve for

First, we need to isolate the term with the exponent on one side of the equation. We can do this by dividing both sides of the equation by.
$\frac{ m^{x+1}}{} = \frac{18}{}$

implify the equation.
$m^{x+1} =6$

To solve for x, we need to remove the exponent. We can do this by taking the logarithm of both sides of the equation. We'll use the natural logarithm (ln) for this.
$ln(m^{x+1}) = ln(6)$

Using the property of logarithms that allows us to bring the exponent down as a multiplier, we rewrite the left side of the equation.
$(x+1) \cdot ln(m) = ln()$

Now, we isolate x by subtracting1 from both sides of the equation.
$x \cdot ln(m) = ln(6) - ln(m)$

Finally, we can solve for x by dividing both sides of the equation by ln(m).
$x = \frac{ln(6) - ln(m)}{ln(m)}$ This is the solution for x in terms of m.