# Pre calculus

posted by .

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 -

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

log_4 x

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.

## Similar Questions

1. ### algebra

logarithms Solve the following equations 3^x-2=6 Add 2 to both sides of the equation to start. Whatever operation you do to one side of an equation you must do to the other side as well. 3^x - 2 + 2 = 6 + 2 3^x = 8 Changing to logs: …
2. ### pre-calculus

What is the base of the function F(x) = b to the power of x if the graph has points of (1/3, 2)and another off the subject one if g(x)= log 7 x what is g(1/49)?
3. ### Math (Logarithms)

How do u do logarithms where there is a log on one side and a number on the other... Example- -21.044=log(P/30) I don't want just an answer to the example, i need to know how to do it please... convert your log equation into an exponential …
4. ### math

solve for x without using a calculator 5^(x+1) = 25 i know that x would equal 1 because 5^2 is 25, but i don't know how to show how to solve it All you need to do is what you just did: Explain that if x = 1, the equation is satisfied. …

6. ### math

when solving the exponential equation, 2^2x-1=16 what do I do first?
7. ### Math - Exponential equation

Solve the exponential equation. Express your solutions in exact form only. Please show all of your work. 5e^(x log(9)) = 11
8. ### Chemistry

How do you do the inverse of absolute temperature?
9. ### Precalculus

This is for solving exponential/logarithmic functions: (This is a base e Logarithmic function I would assume): e^(4x)/10 =4^x-2 ?
10. ### Math

h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h^-1(x) = My work so far h(x) = log(6x+5/7x-4) y=log(6x+5/7x-4) x=log(6y+5/7y-4) 7xy-4x= log(6y+5) how would I solve from here. Would I solve for y then do the …

More Similar Questions