zergingk8l

2022-04-25

Simplifying Logarithmic Expression

Compute:

$\frac{1-{\mathrm{log}}_{a}^{3}b}{({\mathrm{log}}_{a}b+{\mathrm{log}}_{b}a+1){\mathrm{log}}_{a}\frac{a}{b}}$

I tried to expand it :

$\frac{1-{\mathrm{log}}_{a}^{3}b}{({\mathrm{log}}_{a}b+{\mathrm{log}}_{b}a+1){\mathrm{log}}_{a}\frac{a}{b}}$

$=\frac{(1-{\mathrm{log}}_{a}b)({\mathrm{log}}_{a}^{2}b+{\mathrm{log}}_{a}b+1)}{({\mathrm{log}}_{a}b+{\mathrm{log}}_{b}a+1)(1-{\mathrm{log}}_{a}b)}$

$=\frac{({\mathrm{log}}_{a}^{2}b+{\mathrm{log}}_{a}b+1)}{({\mathrm{log}}_{a}b+{\mathrm{log}}_{b}a+1)}$

But I got nothing.

Compute:

I tried to expand it :

But I got nothing.

Cristal Roth

Beginner2022-04-26Added 13 answers

I think this should help you.

$\mathrm{log}}_{b}a=\frac{{\mathrm{log}}_{a}a}{{\mathrm{log}}_{a}b}=\frac{1}{{\mathrm{log}}_{a}b$

Can you finish it from here?

Can you finish it from here?

narratz5dz

Beginner2022-04-27Added 13 answers

You also could use

${\mathrm{log}}_{a}\frac{a}{b}={\mathrm{log}}_{a}a-{\mathrm{log}}_{a}b=1-{\mathrm{log}}_{a}b$

$\mathrm{log}}_{b}a=\frac{1}{{\mathrm{log}}_{a}b$

You can express everything in terms of${\mathrm{log}}_{a}b$ . If you substitute this for readability by, say, x the rest is basic. And to test your result it should be just ${\mathrm{log}}_{a}b$ .

You can express everything in terms of

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$