7 raised to 5x-8 and 5 raised to x+2 if product of these two is equal to 30625 then how to find value of x

:)

simplify log base 3 of 243^2

a^x =b^y = c^z = abc ; find 1/x + 1/y + 1/z

Taking logs then dividing we can see that... 

 
from which we deduce 
 
similarly 

and
 
therefore 
 
i.e. 

Make n the subject of the formula given that PV^n=c

write as a single logarithm: 2 ln x - 3 ln y + 1/3 ln z

If log 94.3 is 1.9745 then log 0.0943 =

Recall that  and since 0.0943=94.3/100, we can write 

log5(12). How would you do it on the calculator?

Use log base conversion...check your textbook for details...
log(12)/log(5)=ln(12)/ln(5)=1.543...

find the value of x log3 x = 4

Your Answer:

the inverse to

 is 

so we raise both sides of the equation to 3


 

What is the logaritmic form of the equation 3^x= 12

We will use the inverse property of logs to help us 

 

has a base of 3 so we use log base 3 which we'll denote by 

 

 

 


:)

Evaluate the logarithmic expression

How do I expand ln5x^6/11y^7 ?

Simplify: Log5(15/0.45)

log5(100/3)=

log5(25)+log5(4/3)=
2+log5(4)-log5(3)

how do you write ln4-2ln(1/2) as a single logarithm

ln4-2ln(1/2)=
ln4+2ln2=
ln4+ln4=
2ln4

how do i do this: 1 /loga(abc) +1 /logb(abc) +1 /logc(abc) ?

use the change of base identity: 
1 /loga(abc) +1 /logb(abc) +1 /logc(abc)=
(log(a)+log(b)+log(c))/log(abc)

simplify: ln 3 - 2(ln 4 + ln 8)

ln 3 - 2(ln 4 + ln 8)= 
ln(3/(4*8)^2)=
ln(3/1024)

Simplify 2^(log2(8))

the two functions are inverses so the result is 8

what is the approximate value of log10(225), given that log2 is 0.301 and log5 is 0.698

 

:)

Write the exponential equation in logarithmic form

Logarithms

How do you find 10^(1/10) without a calculator?

Solving this problem by hand could be a formidable task depending upon the method of solution. Let's assume we are only restricted from directly using a calculator and we are allowed to use tables, and we can check our progress with a calculator. Furthermore we'll assume that we want a relatively easy way to do this, but we are willing to need to do a lot of handwork. First we do some algebra:

Next we consult logarithm tables by searching for what value of log(x) is closest to 0.1. A careful search puts us between 1.25 and 1.26. That is to say: log(1.25)=0.09691 and log(1.26)=0.1003705

Averaging these two results yields: log(1.255)=0.09864025. The actual value is log(1.255)=0.0986437258, so that's not too bad!

From this we deduce that 0.09864025 < log(x) < 0.1003705, which tells us that log(1.255) < log(x) < log(1.26).

By repeating this process we can muddle our way to a decent approximation.

The value is not rational but here are 20 decimals: log(x)=1.2589254117941672104