Can someone explain relationship between exponents and logarithms
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Can someone explain relationship between exponents and logarithms

[From: ] [author: ] [Date: 11-12-13] [Hit: ]
Clearly, the power that we must raise 17 to to get 17^x is x. Thereforelog17(y) = xMy calculator doesnt have a log17 button, so Id like to convert that into log10, which thankfully is as easy as rewriting it like solog10(y) / log10(17) = xor in shorthandlog(y) / log(17) = xSo if I ever need to raise 17 to a power and hit some target number y, thats how I do it.......

log17(y) = log17(17^x)

Log base 17 will tell us the power that we have to raise 17 to, to get some number. In this case, that number is 17^x. Clearly, the power that we must raise 17 to to get 17^x is x. Therefore

log17(y) = x

My calculator doesn't have a log17 button, so I'd like to convert that into log10, which thankfully is as easy as rewriting it like so

log10(y) / log10(17) = x

or in shorthand

log(y) / log(17) = x

So if I ever need to raise 17 to a power and hit some target number y, that's how I do it. You can see it works by plugging in, say, 1400 for y:

log(1400) / log(17) = 2.55689446...
17^2.55689446... = 1400

When I ask my question, "To what exponent must I raise this base to get some number?" the log function tells me an answer which is an exponent. Because logs always spit out exponents, all the cool tricks we have for working with exponents are true for logs as well. For example

10^a * 10^b = 10^(a+b)
just like

log(a) + log(b) = log(a*b)

and some other cool things.


edit-

log(base 10)(3x+5) = 8

to solve this, we go the other way. log10(3x+5) asks, 10^? = 3x+5
Without knowing what that question mark is, if we raise 10 to that power, we get 3x+5. So let's simplify by raising 10 to both sides of the equation-

10^(log10(3x+5)) = 10^8
and rewrite to simplify
3x+5 = 10^8 = 100000000

then we can solve by algebra. x works out to be about 33333331.66666667

You can check your work by plugging that back into the original equation

log( ( 3 * 33333331.7 ) + 5) = 8

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Logs are the inverse of exponents. Log base b of (y)= x is the same as b^x=y.
So log base 10 of y=2 is the same as 10^2=y so y=100.
Graphically, they are inverses.
The best technique is probably to use the two equations above to convert between logarithmic and exponential form.

Log10 is just when the base or b is equal to 10. This is what is used on calculators. You type I. Log(y) and it's already in base 10.
e is just like pi but it's 2.71828..... It goes on forever.

Maybe try: purplemath.com/modules/solvexpo2.htm

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Log 10 is just the basic form. Like Most would be in the format of Log (# below) and then a big #. Logrythams and exponents can convert into eachother like log5 3=12 converts to 5^12=3

I know the numbErs Don't actually make sense but that's the form. The 5 I put after log.. remember those are always carrot down ( the opposite of ^) however my phone doesn't make that symbol

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A logarithm is an exponent.
log(base b)a = c if and only if b^c = a.
lna = c if and only if e^c = a
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