Question

Keisha is solving the equation 7 to the power of x equals 9. Which equation shows the first step she should take?

Answer 1

Answer:

The correct answers are:

Question 4: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: step 4 could be n ln 2 equals ln 86

Question 6: the exact solution is x=ln(7)

Step-by-step explanation:

Ok,

Question 4: the equation that shows the first step Keisha should take is:

$7^{x}=9$

$log(7^{x} )=log(9)$

$x(log(7))=log(9)$ (applying the properties of logarithms)

$x=\frac{log(9)}{log(7)} =1.129$

Solution: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: Her first three steps are:

$2^{n}-3=83$

$2^{n}-3+3=83+3$ (adding 3 to both sides)

$2^{n}=86$

$2^{n}-3+3=83+3$

$nln(2)=ln(86)$

Solution: step 4 is: $nln(2)=ln(86)$ (applying the properties of logarithms)

Question 6: The exact solution of 2 e to the power of x equals 14 is:

$2e^{x}=14$

$\frac{2e^{x} }{2} =\frac{14}{2}$ (dividing both sides by 2)

$e^{x}=7$

$xln(e)=ln7$ (ln(e)=1)

$x=ln(7)$

Solution: $x=ln(7)$