Posted by marcus on Tuesday, November 20, 2012 at 10:48am.
Okay, I'm really fuzzy about my log and exponential chapter. For example, solving some exponential equation such as e^3x-7 x e^-2x=4e
I assume I start this equation by taking the natural log of both sides, but how will I know just by looking at an equation weather I need to find the log or the natural log?
Also, graphing. How to do you know where to put the base graph? Such as f(x)= log_1/2_x?
- Pre calculus - Steve, Tuesday, November 20, 2012 at 11:05am
Usually you take logs to the base of the number having exponents. In your example, you have e^(3x-7), so take logs base e.
If you had written 2^(x+3) * 2^(x-7) = 32 then you'd take logs base 2.
As for graphing, just recall the all exponent/log graphs look the same, except for their slopes.
e^x looks just like 10^x. They both go through (0,1). e^x goes through (1,e) and 10^x goes through (1,10).
Fractional bases are just reflected through the y-axis, since (1/2)^x = 2^-x.
Now, logs look just like exponentials, but reflected through the origin, since if
y = e^x,
x = ln y
fractional bases are reflected through the x-axis.
So, as for log_1/2(x) It looks like log_2(x) but upside-down.
Visit wolframalpha.com and enter
or whatever base you want. It will also remind you that log_4(x) = lnx/ln4.
This also explains the reflection using fractional bases. log_1/2(x) = lnx/ln 1/2, and ln 1/2 is negative.
Answer this Question
More Related Questions
- Math (Logarithms) - How do u do logarithms where there is a log on one side and ...
- Math - Exponential equation - Solve the exponential equation. Express your ...
- math - when solving the exponential equation, 2^2x-1=16 what do I do first? do I...
- algebra - logarithms Solve the following equations 3^x-2=6 Add 2 to both sides ...
- Logs. - Can you please help me with the following log. problems? thanxs! Solve ...
- Precalculus - This is for solving exponential/logarithmic functions: (This is a ...
- Logarithms - Kepler's third law of planetary motion relates P, the period of a ...
- pre-calculus - What is the base of the function F(x) = b to the power of x if ...
- Pre-Calc/Trig... - Write the equation y = log x in exponential form.
- math - Logarithm!!! Select all of the following that are true statements: (a) ...