Unit 4 Review: Exponentials and Logarithms

Flashcards based on the key concepts from the Unit 4 Review lecture notes on Exponentials and Logarithms.

How do you write 43 = 64 in logarithmic form?

log(64) = 43

How do you express log(7) = 13 in exponential form?

7^13 = x

How can you condense the expression log(16) - 2log(5) + logb(7) into a single logarithm?

log(16/25) + logb(7) = log(16b(7)/25)

What is the result of condensing log2(x-2) + log2(x+2)?

log2((x-2)(x+2))

How do you expand log(x)?

log(x) = log(x) (it is already in expanded form).

What is the expanded form of In(x + 1) + In(x-1) + In(x)?

In((x + 1)(x - 1)x)

What is the solution for the equation 81* = 9x + 2?

Solve for x depending on given values.

How do you solve for x in the equation 7log7(x) = 3?

x = 7^(3/7)

What is the value of log16(x) = 125?

x = 16^125

If log4(x^3 + 6x^2) - log4(x) = 2, what is x?

x = 10 or any suitable value based on context.

For the equation y = 2x + 4, what are its intercepts and asymptote?

x-intercept = -2, y-intercept = 4, no asymptote.

What is the x-intercept of the equation y = e^(x-1) - 1?

Solve e^(x-1) = 1 for x.

How do you determine the y-intercept of the equation y = log2(x-2)?

Substitute x = 2.

For the equation 27* = 34, how do you solve for x?

Take the logarithm of both sides and solve.

What is the solution of the equation 16 = 27x-5?

Rearrange and solve for x.

Solve for x in the equation log(3x + 7) + log(x - 2) = 1.

Combine using properties of logarithms and isolate x.

What do you do to solve the equation 32x = 81?

Take log and solve for x.

What do you find when solving 16* = (23)4?

Express in base 2 and compare exponents.

How do you solve the equation log6(x - 5) + log6(x) = 2?

Combine logs and solve for x.

What is the expression for loga(x)?

This will depend on specific values given.

For the equation 72x = 493x + 1, how do you solve for x?

Isolate x and use logarithmic properties to solve.