Question

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1. what is the exponential form of the following: ln(x+2)=10

2. express the following as a sum or difference in logarithms: 1. lnx/(x+3)^3 2. log_6 a^4b^3/c^2

3. what is the logarithmic form of the following equation: 5^y-2 = 125

Answer 1

See below

Explanation:

1.........................................................

• ln(x+2)=10
• x + 2 = e¹⁰

2.........................................................

1)

• ln x / (x + 3)³ =
• ln x - ln (x + 3)³ =
• ln x - 3ln(x + 3)

2)

• log₆ a⁴b³/c² =
• log₆ a⁴ + log₆ b³ - log₆ c² =
• 4log₆ a + 3log₆ b - 2log₆ c

3. .........................................................

note: replaced y with n

• 5ⁿ⁻² = 125
• 5ⁿ⁻² = 5³
• log 5ⁿ⁻² = log 5³
• (n - 2) log 5 = 3 log 5
• n - 2 = 3
• n = 5