Express Logarithms and Exponential Expressions
Express 43 = 64 in logarithmic form:
logbx = y
log464 = 3
State the transformation(s) of the following function:
f(x) = log(x)+10
Vertical translation by 10 units up
Use the properties and laws of log to answer:
log2416 + log2436
A: x = 2
Solve the following equation:
12209 = 2.5n
A: n=10.27
Research was conducted to test the noise levels in school gymnasiums. Loudness levels ranged from 75 dB to 115 dB. How many times as loud as noise at 75 dB is a noise at 115 dB?
A: 10 000 times
Express logx(128) = 7 in logarithmic form:
x7 = 128
State the log function given its transformations:
- Horizontal shift by 3 units right
- Vertical translation 3 units down
f(x) = log (x-3)-3
Use the properties and laws of log to answer:
log51254
A: x = 12
Solve the following equation:
243q = 27-3q+1
A: q = 3/14
On October 20, 1965, an earthquake with a magnitude 5.8 hit Miami, Florida. On the next day, a second earthquake with magnitude 6.0 hit the same region. How many times as intense as the first earthquake was the second earthquake? Round to the nearest hundredth.
A: The second earthquake was approximately 1.58 times more intense than the first one.
Determine an expression for x in logarithmic form.
73x = 12
73x = 12
3x = log712
x = (log712)/3
Given the function y=-log(x+1)+2, state the 3 transformations of this curve.
1. -log ->reflection in the x-axis
2. +1 -> horizontal translation 1 unit to the left
3. +2 -> vertical translation up 2 units
Use the properties and laws of log to answer:
log3√45 - log3√5 + log3√25
A: log315
Solve the following equation:
log3(x-2) + log3(x) = 1
A: x=3
x ≠ -1 <--- extraneous root, cannot be true
Use different expressions to create two logarithmic functions that have the same graph. Demonstrate algebraically why these functions have the same graph. Explain your reasoning and justify your answer.
A: answers may vary
Write the logarithm as an exponential expression:
x = (log624)/3
x = (log624)/3
3(x) = log624
63x = 24
Determine the x and y intercept of y=log(x-2)+1
xint = (-1.9 , 0)
yint = (0 , 1.3)
Rewrite logarithm expression:
log8 ((6√r5 • s3)/t2)
(hint: logax)
A: 5/6log8r + 3log8s - 2log8t
Solve the following equation:
3log2x - log2x = 8
A: x=16
x≠-16 <---- extraneous root, cannot be true
Calculate the hydrogen ion concentration of each substance:
A) Fruit punch, with a pH of 3.6
B) Cabbage, with a pH of 6.9
C) Stove cleaner, with a pH of 12
A: A) 3.16 x 10-4.1 mols/L
B) 3.16 x 10-7.4 mols/L
C) 3.16 x 10-12.5 mols/L
Write the logarithm as an exponential expression:
x = (log8120)/-6
x = (log8120)/-6
-6(x) = log8120
8-6x = 120
The function, f(x) = log10x has the point (10,1) on its graph. If f(x) is vertically stretched by a factor of 3, reflected in the x axis, horizontally compressed by a factor of 2, horizontally translated 5 units to the right and vertically translated 2 units up, determine
a) equation of the transformed function
b) domain and range of the transformed function
c) equation of the vertical asymptote
A: a) -3og10[1/2(x-5)]+2
b) D = {x|x>5, x∈R}
R = {y|y∈R}
c) VA: x=5
Determine the horizontal and vertical asymptotes and domain for y=-log(x+3)-4
Horizontal asymptote -> x=infinity
Vertical asymptote -> x=-3
Domain -> x>-3
Solve the following equation:
1 - log(x-4) - log(x+5) = 0
A: x=-6 and 5
The population of Delhi, India can be modelled by the function, P(t)= 9817(1.031)t where P(t) is in thousands and t is the number of years since 2001.
A) Predict the population in 2018.
B) If this growth rate continues, in what year will the population reach 15 million people?
A: A) 16 495.903
B) 2014 (Approximately 13. 9 years later)