SOLUTION: I am so confused with this problem.
Express as a sum, difference, and product of logarithims, without using exponents.
3
log b √ x^8/y^2z^5
I could not get i
Algebra.Com
Question 212356: I am so confused with this problem.
Express as a sum, difference, and product of logarithims, without using exponents.
3
log b √ x^8/y^2z^5
I could not get it to show the way the problem does. It reads log (small b below) square root with 3 above the square root symbol. Inside the square root symbol it has x^8 over y^2z^5.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Express as a sum, difference, and product of logarithims, without using exponents.
3
log b √ x^8/y^2z^5
I could not get it to show the way the problem does. It reads log (small b below) square root with 3 above the square root symbol. Inside the square root symbol it has x^8 over y^2z^5.
------------------------
log(base b) [x^8/y^2*z^5]^(1/3)
-----
= (1/3){log(b)[x^8] - log(b)[y^2z^5]}
---
= (1/3)[8log(b)x - [2log(b)y + 5log(b)z]}
---
= (8/3)log(b)x - (2/3)log(b)y - (5/3)log(b)z
===================================================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
)
... Start with the given expression.
^{\frac{1}{3}} \right))
... Convert to rational exponent notation.
)
... Pull down the exponent using the identity
-\log_{b}\left(y^2z^5\right) \right))
... Break up the log using the identity
-\left(\log_{b}\left(y^2\right)+\log_{b}\left(z^5\right)\right) \right))
... Break up the second log using the identity
-\log_{b}\left(y^2\right)-\log_{b}\left(z^5\right) \right))
Distribute
-2\log_{b}\left(y\right)-5\log_{b}\left(z\right) \right))
... Pull down the exponents using the identity
-\frac{2}{3}\log_{b}\left(y\right)-\frac{5}{3}\log_{b}\left(z\right))
... Distribute
So
 = \frac{8}{3}\log_{b}\left(x\right)-\frac{2}{3}\log_{b}\left(y\right)-\frac{5}{3}\log_{b}\left(z\right))
assuming that every variable is positive.
RELATED QUESTIONS
express as a sum, difference, and a product of logarithms, without using exponents.... (answered by london maths tutor)
Express as a sum, difference, and product of logarithms, without using exponents.... (answered by MRperkins)
Express as a sum, difference, and product of logarithms, without using exponents.
log (answered by rapaljer)
1.Solve the problem.
Given log b 3 = 3.6887 and log b 7 = 1.4873.
Find logb 3/7... (answered by stanbon)
Please help and let me know if i am correct! thank you
Express as a sum, difference, and (answered by edjones)
express as (all three) a sum, difference and product of logarithms, without using... (answered by Edwin McCravy)
Express as a sum, difference, and product of logarithms, without using exponents.
log... (answered by london maths tutor)
{{{ log(b, ((x^5b^9)/(y^7z^10))^(1/4)) }}}
Express as a sum, difference, and product... (answered by malaydassharma)
Hi,
Can you help me with solving this problem?
Express as a sum, difference, and... (answered by stanbon)