Properties of Exponents and Logarithms Exercises
Example 1
Combine the following log functions into one function:
log 4 + log(x – 3) + log(2x + 4)
Example 2
Is the following expansion of a logarithmic expression correct?
log(9x + 4) = log(9x) + log 4
Example 3
Is log4 16 equivalent to 2 log4 8?
Example 4
Combine the following log functions into one function:
log 7 – log(8x) – log(4x + 6)
Example 5
Combine the following log functions into one function:
log x2 + log y – log y2
Example 6
Solve e6xe -7x = y for x.
Example 7
Expand the following log function:
log5(4xy)
Example 8
Expand the following log function, then simplify irrationals to three decimal places:
.
Example 9
Simplify the following log function to a form without exponents, then change to base-10:
y = log7(100x2)
Example 10
Convert the following exponential equation to natural logarithmic form, then simplify irrationals to three decimal places:
y = ex4x
Example 11
Simplify the following log function so there aren't any squared terms:
log(x2 + 4x + 4)
Example 12
Simplify the following log function and solve for z:
4 = log x2 + log y + log z
Example 13
Expand the following log function:
ln[(4x2y)/(z1/2)]
