Solve the following exponential equation for y:
7(y + 1) = 3x + 3
Hint
Take the log of both sides, but which log?
Answer
y = log7(3x + 3) – 1
Find x in the following exponential equation. Do not simplify to decimals:
4ex + 10 = 20
Isolate ex first.
x = ln 5/2
What value of x satisfies the following equation?
log10 10 = x
What does x represent in the exponential form?
x = 1
log3 1 = x
Any (arguably non-zero) number can be raised to a particular value to get an answer of 1. What power is it?
x = 0
Is the following logarithmic equation valid for any one value of x?
log10 x = -3
Can a base have a negative exponent?
Yep, x is simply
e(y + 4) – 15 = x2
Isolate e(y + 4) first, then bust out the natural log.
y = ln(x2 + 15) – 4
Solve the logarithmic equation for x. Do not simplify to decimals.
Convert to an exponential equation first.
or
Evaluate the following log equation for x = 9:
y = log3(x2)
What exponent do we need to stick on a base of 3 to get 92 as our answer?
y = 4
Evaluate the following log equation for x = 5, to three decimal places:
y = ln(3x) + ln(ex)
One ln can be simplified first.
y ≈ 7.708
Evaluate the following log equation to three decimal places using only base-10 logarithmic functions:
y = log3 13
Use the change of base formula.
Write log4 17 in base-10 form.
Write ln(4x) in base-10 form.
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for x. Do not simplify to decimals.
or 
