Which logarithmic equation is equivalent to the exponential equation below?
e^a=38.47

a. in a=38.47
b. log a 38.47=3.65
c. in 38.47= a
d. log38.47 3.65=e

C)  a =  ln (38.47).

Step-by-step explanation:

Given : = 38.47

To find : Which logarithmic equation is equivalent to the exponential equation.

Solution : We have given that : = 38.47.

Taking natural logarithm both sides

= log(38.47).

By the  logarithm rule: ; =1.

Then , a =  ln (38.47).

Therefore,C)  a =  ln (38.47).

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!