Question

Show the steps you took to get to the answer please and thank you so much!

Write the exponential form: log₅125=3

Write in logarithmic form square root of 36=6

Write as a single logarithm:

6 log x + 2 log y

ln 7 - 3 ln x

Solve each equation:

400e^0.005x=1600

log₆(4x-1)=3

2ln(3x)=8

log x + log(x+15)=2

simplify the expression:

lne_5x

Answer 1

1)

log ₅ 125 = 3

changing logarithmic form to exponentiao firm by using log property

log _a (x) = y

x = a^y

applying this property our equation becomes

125 = 5^3

2) sqrt 36 = 6

sqrt = raised to power 1/2

so we can write

36 ^1/2 = 6

taking log on both sides

1/2 log 36 = log 6

3) 6 log x + 2 log y

writing as single logarithm by applying log property

a log m = log m^a

so, 6 log x + 2 log y = log x^6 + log y^2

addition becomes multiplication when condensing

log x^6 + log y^2 = log ( x^6 y^2 )

4) ln 7 - 3 ln x

ln 7 - ln x^3

subtraction beocmes division when condensing

ln 7 - ln x^3

= ln ( 7/x^3 )