Question

PLEASE HELP ASAP
Mike is working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.

Hint: Use the change of base formula: log base b of y equals log y over log b.

Answer 1

Answer:

See below

Step-by-step explanation:

I presume you meant $37^x=12$

Exponential equation has the following form:

$y = a {b}^{x}$

To solve exponential equation, the steps are as follows:

1. Take either natural or common logarithm
2. Apply the exponent rule of logarithm
3. divide both sides by the constant of x
4. use the change of base formula

How should Mike solve the equation?

Firstly Mike should take common logarithm in both sides. Secondly he should apply the exponent rule of logarithm. Thirdly he should divide both sides by the constant of x. Finally he should apply the change of base formula. See below

$\\ {37}^{x} = 12 \\\\ [ \text{step - 1}] \\\\ \log( {37}^{x} ) = \log(12 )\\\\ [ \text{step - 2}] \\ \\ x \log(37) = \log( 12) \\ \\ \text{[step - 3}] \\ \\ x = \dfrac{ \log(12)}{ \log(37)} \\ \\ [ \text{step - 4}] \\ \\ \boxed{x = \log_{37}(12) }$

Answer 2

The whole solution is on assumption as the question is not clear especially the equation part

$\\ \rm\Rrightarrow 3(7^x)=12$

How to solve?

• First simplify the expression by taking 3 to right

$\\ \rm\Rrightarrow 7^x=\dfrac{12}{3}$

$\\ \rm\Rrightarrow 7^x=4$

• Now apply common logarithm on both sides

$\\ \rm\Rrightarrow log7^x=log4$

Use the rule

• loga^b=bloga

$\\ \rm\Rrightarrow xlog7=log4$

• Divide both sides by log7

$\\ \rm\Rrightarrow x=\dfrac{log4}{log7}$

• Use change of base formula

$\\ \rm\Rrightarrow x=log_7(4)$

Accurate value

$\\ \rm\Rrightarrow x=0.7124143742160$