Combine the following log functions into one function:
log 4 + log(x – 3) + log(2x + 4)
Hint
Rock the distributive property.
Answer
log(8x2 – 8x – 48)
Is the following expansion of a logarithmic expression correct?
log(9x + 4) = log(9x) + log 4
Try solving the logs for a specific value of x.
Nope. We can't separate terms in a logarithm into individual logarithms.
Is log4 16 equivalent to 2 log4 8?
Use the "exponent in log" rule to mess with log4 16.
No! That first expression is equivalent to 2 log4 4.
log 7 – log(8x) – log(4x + 6)
Use the difference of logarithms property.
log x2 + log y – log y2
Use the difference and sum of logarithms properties.
Solve e6xe -7x = y for x.
Try combining the bases first, and then bust out the natural log.
x = -ln y
Expand the following log function:
log5(4xy)
Use the sum of logarithms property.
log5 4 + log5 x + log5 y
Expand the following log function, then simplify irrationals to three decimal places:
A square root is equivalent to a power of .
Simplify the following log function to a form without exponents, then change to base-10:
y = log7(100x2)
How can you pull the exponent outside of the logarithm?
Convert the following exponential equation to natural logarithmic form, then simplify irrationals to three decimal places:
y = ex4x
Start by taking the natural log of both sides, then separate the log.
ln y = 2.386x
Simplify the following log function so there aren't any squared terms:
log(x2 + 4x + 4)
Start by factoring that quadratic inside the log.
2log(x + 2)
Simplify the following log function and solve for z:
4 = log x2 + log y + log z
Use the exponential form.
ln[(4x2y)/(z1/2)]
Try separating into four natural logs to start.
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