A Simplify the expression please show your work the answer s

(A) Simplify the expression

please show your work the answer should be a rational number

(B) Slove

10_e^3x = 50

First find the exact solution, and then approximate it to 2 decimal digits.

Solution

A. log_1/354   - log_1/32sqrt3

We have to use the following log property

log a - log b= log(a/b)

log_1/354 - log_1/32sqrt3= log_1/3(54/2sqrt3)

                                      = log_1/3(1/(3)^-5/2)

log a^b=b log a

So we get log_1/3(1/3)^-5/2= -5/2 log_1/31/3 = -5/2

b. 10e^3x=50

    e^3x=5

    Taking ln on both sides

     3x= ln 5

    x= ln5/3   ,that\'s the exact solution

     x=.54