1108
Yes. log( a * b ) = log(a) + log(b). This law is the inverse of the law of exponents x^(y + z) = x^y + x^z.
Yes. log(a^b) = b log(a). This law is the inverse of the law of exponents (x^y)^z = x^(yz).
No. log( a * b ) = log(a) + log(b). This law is the inverse of the law of exponents x^(y + z) = x^y + x^z.
No. log(a^b) = b log(a). This law is the inverse of the law of exponents (x^y)^z = x^(yz). Also log(a*b) = log(a) + log(b), as we saw earlier.
Yes.
log(a / b) = log(a * b^-1)
= log(a) + log(b^-1)
= log(a) + (-1) log(b)
= log(a) - log(b).
Yes. log( a * b ) = log(a) + log(b). This law is the inverse of the law of exponents x^(y + z) = x^y + x^z.
No.
log(a / b)
= log(a * b^-1)
= ...
= log(a) - log(b).
No. log( a * b ) = log(a) + log(b). This law is the inverse of the law of exponents x^(y + z) = x^y + x^z.
Yes. log(a^b) = b log(a). This law is the inverse of the law of exponents (x^y)^z = x^(yz).
Yes. b * log(a) = log(b *a).
Yes. This law is the inverse of the law of exponents (x^y)^z = x^(yz).
No. log(a) - log(b) = log(a/b)
Yes. Since 20 = 4 * 5, log(20) = log(4 * 5) = log(4) + log(5).
No. 4 log(5) = log(5^4) = log(625), not log(1024).
Yes. 5 log(4) = log(4^5) = log(1024).
On our table 7857 is between 1000 and 10,000 so the log is between 3 and 4.
The log of the number halfway between 1000 and 10,000 is more than halfway from 3 to 4, so the log of 7857 is clearly closer to 4 than to 3.
Solve the equation 5^(2x-4) = 79.
log(20) = log(4) + log(5)
log(1024) = 5 * log(4)
log(7284) is between
log(.00874) is between
y = log{base 10}(x) vs. x is inverse to y = 10^x vs. x. The tables are inverse, the graphs are inverse. You should be able to make a basic table and graph for both functions in 2 minutes or less.
Make a table of y = 10^x vs. x, then invert it to make a table of y = log{base 10}(x) vs. x. Sketch a quick graph of log{base 10}(x) vs. x.
What are log(100), log(.001) and log(10,000)?
log(100) = 2, easily read from the table. This happens because 10^2 = 100, which should be clear from looking at both tables.
Similarly, log(.001) = -3 because 10^-3 = .001.
log(10,000) = 4, easily figured by extending the table. This is so because 10^4 = 10,000.
Estimate log(50), log(-.3), log(.3) and log(7000).
50 lies between 10 and 100, so log(50) lies between log(10) = 1 and log(100) = 2. We might guess about halfway: maybe log(50) = 1.5. This is a pretty good guess.
Looking at the concavity of the graph we see that the actual value is probably a little higher, or about 1.7.
Use your calculator to find log(50), log(-.3) and log(7000).
What is 10^2.4? What is the log of this number?
What would you get if you took the log of both sides of the equation 10^(2x - 3) = .001?
We would get
log(10^2.4) = 2.4, log(10^aardvark) = aardvark, and log(10^(2x-3) ) = 2x - 3.
log(.001) = -3, since 10^-3 = .001.
So our equation becomes
Laws of exponents:
10^(a + b) = 10^a * 10^b
(10^a)^b = 10^(ab).
Laws of logarithms turn these laws around:
log(a * b) = log(a) + log(b)
log(a^b) = b * log(a).