Solving logarithmic equations

Solving logrithmic equations

What is a logarithm?

• the inverse of an exponent

• which means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x

Logarithms explained ...

https://www.youtube.com/watch?v=zzu2POfYv0Y

Two forms

1. exponential

2. logaerithmic

Multiple Choice

Rewrite in exponential form:

log₂ 0.25 = -2

• -2² = 0.25

• -2^0.25 = 2

• 2^-2 = 0.25

• No correct answer

Multiple Choice

Rewrite in logarithmic form:

6² = 36

• log₆ 2 = 36

• log₆ 36 = 2

• ln 36 = 2

• 6³⁶ = 2

Multiple Choice

Rewrite in exponential form:

log₃(9)=2.

• 3⁹=2

• 3²=9

• x²=9

• 3^x=2

Multiple Choice

Rewrite in logarithmic form:

5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5

Multiple Choice

y = 2^x

If y = 3, approximately what is x?

Round to 4 decimal places.

• 2.0000

• 1.3454

• 1.5850

• 1.8580

• 0.6309

Explanation

To solve, we use logarithms. We log both sides and get: log3 = log2^x

which can be rewritten as log3 = xsalog2

Then we solve for x: x = log 3/log 2 = 1.5850 . . .

Multiple Choice

If log_x49=2, what is x?

• 0

• 2401

• 10

• 24.5

• 7

Explanation

If log_xy=z, then x^z=y

x²=49

x=7

Multiple Choice

If log₄ x = 2, what is the square root of x?

• 16

• 4

• 2

• 12

• 3

Explanation

Given log₄x = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.

Multiple Choice

Solve for x in the following equation:

log₂24 - log₂3 = log_x27

• 16

• 32

• 2

• 8

• 4

Explanation

The general equation of a logarithm is log_xa=b, and x^b=a

In this case, x²=64, and thus x=8 (or −8, but −8 is not an answer choice)

Questions?