Question

Solve 3x + 2 = 15 for x using the change of base formula log base b of y equals log y over log b. −1.594 0.465 2.406 4.465

Answer 1

Answer:

0.465

Step-by-step explanation:

Solve 3x + 2 = 15 for x using the change of base formula log base b of y equals log y over log b. −1.594 0.465 2.406 4.465

rearranging the question

$3^{x+2} =15$.........1

the change of base in logarithm is given by.

$log_{b} a=\frac{loga}{logb}$

back to equation 1

taking logarithm of the other end

x+2=$log_{3} 15$

x+2=log 15/log 3

also

we could write

x+2(log3)=log15

x+2=2.465

x=2.465-2

x=0.465

Answer 2

Answer:

The value in 3x + 2 = 15 for x using the change of base formula is 0.465 approximately and second option is correct one.

Solution:

Given, expression is $3^{(x+2)}=15$

We have to solve the above expression using change of base formula which is given as

$\log _{b} a=\frac{\log a}{\log b}$

Now, let us first apply logarithm for the given expression.

Then given expression turns into as, $x+2=\log _{3} 15$

By using change of base formula,

$x+2=\frac{\log _{10} 15}{\log _{10} 3}$

x + 2 = 2.4649

x = 2.4649 – 2  = 0.4649

Hence, the value of x is 0.465 approximately and second option is correct one.