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Rewriting Logarithms and Exponentials
Solving Logarithmic Equations
Expanding & Condensing Logs
100
Write the exponential equation 4^5= 1,024 in logarithmic form.
What is log (base 4) 1,024 = 5 ?
100
Solve: log(base 1/7)(7x+3)=log(base 1/7)(2x+13)
What is x=2
100

Expand log(x)^(1/3) into multiple logs.

What is (1/3)log x

200
Write the exponential equation 27^ (1/3) = 3 in logarithmic form.
What is log (base 27) 3 = 1/3 ?
200
Solve: log (base 3) x = 5
What is x = 243 ?
200

Condense 2log (base 5) x + 12log (base 5) y into a single log.

What is log (base 5) x^2 * y^12

300
Write the exponential equation (1/2)^-3=8 in logarithmic form.
What is log (base 1/2) 8 = -3
300

Solve: log(base 5)25x^(3)

What is 5

300

Condense log (2x) + log (3x) - log (x) into one single log.

What is log (6x)

400

Write the log equation log (base n) m = - 6 into exponential form.

What is n^-6 = m

400

Solve: log (base 7) 4 + 2log (base 7) x = log (base 7) 36

What is x = 3

400

Expand log (base 8) x^4 / (y^9 * z^7) into multiple logs.

What is 4log (base 8) x - [9log (base 8) y + 7log (base 8) z]

500

Write the log equation log (base y) 77 = x into exponential form.

What is y^x = 77

500

Solve: log (base 3) 27 - log (base 3) (x - 1) = 2

What is x = 4

500

Expand log (base 3) (a^3 + b^7)

What is cannot expand? Needs to be multiplication or division into order to expand.