Laws of Logarithms

If 3^x = y, which of the following is true?

• log₃y = x
• log₃x = y
• log_xy = 3
• log_y3 = x

Tags

CCSS.HSF.BF.B.5

If log_a8 = b, which of the following is true?

• a^b = 8
• b^a = 8
• a⁸ = b
• 8^b = a

Tags

CCSS.HSF.BF.B.5

Simplify log(12) + log (6)

• log(72)
• log(18)
• log(6)
• log(2)

Simplify: log(3) + 2log(5)

• log(75)
• 2log(15)
• log(30)
• log(13)

Simplify: 2log(x) + 3log(xy)

• log(x⁵y³)
• log(5xy)
• 5log(x²y)
• log(6x²y)

Simplify: log(24) - log(8)

• log(3)
• log(16)
• 4log(2)
• -log(32)

Simplify: log(16) - 3log(2)

• log(2)
• log(10)
• -3log(8)
• 3log(14)

Simplify: 3log(xy) - 2log(x)

• log(xy³)
• log(y)
• 1.5log(x²y)
• Can't be simplified

What is the most simple answer possible:
log_x(x³y) - log_x(xy)

• log_x(x²)
• 2
• log_x(x⁴-y²)
• x

Solve for x:
log(3x-1) - log(5) = 2

• x = 167
• x = 500
• x = 2
• x = 3.67