Question

What is the relation between 'a' & 'b': -

Answer 1

\[\color{red}{\log_{10}{a}+\log_{10}{b}=\log_{10}{(a+b)}. }\]

Answer 2

The answer given is \[\color{blue}{a=\frac{b}{b-1}.}\]

Answer 3

\[\huge{log(mn)=log_m+log_n}\]
\[\huge{a+b=ab}\]

Answer 4

can u do it now ?

Answer 5

correction\[\huge{\log_b (mn)=\log_bm+\log_b n}\]

Answer 6

sorry for that mistake @lalaly

Answer 7

its ok :D

Answer 8

no:/
I m not getting my answer from this formula actually @mathslover @lalaly

Answer 9

lol Lana is never unfair :P

Answer 10

wait

Answer 11

k:)

Answer 12

\(\huge{log(a)_{10}=\frac{{log a}}{log10}}\)

Answer 13

k! i know this:)

Answer 14

\[\huge{\log_a{10}=\frac{{\log_b{10}}}{\log_b{10}}}\]I think it is like this.

Answer 15

sorry @ denominator should be "a"

Answer 16

use the rules of logarithms
http://www.sosmath.com/algebra/logs/log4/log44/log44.html
when u see a sum of two logs with the same base
\[\huge{\log _R U+\log_R V =\log_R (UV)}\]so in ur question u have log a with base 10 and log b with base 10 ... so that is equal to the log of the multiplication of a and b\[\log_{10}a+\log_{10}b=\log_{10}(ab)\]
equal that to the two whats given to u
\[\log_{10}ab =\log_{10}(a+b) \]and that is equal to
\[ab=a+b\]solving for a\[ab-a=b\]\[a(b-1)=b\]\[a=\frac{b}{b-1}\]

Answer 17

k! thanx a lot @lalaly

Answer 18

thank @mathslover :D

Answer 19

xD

Answer 20

log^10(a)+log^10(b)=log^10(a+b)

Move all the terms containing a logarithm to the left-hand side of the equation.
log^10(a)+log^10(b)-log^10(a+b)=0

Combine the logarithmic expressions using the product rule of logarithms.
log((a)(b))-log^10(a+b)=0

Combine the logarithmic expressions using the product rule of logarithms.
log(((a)(b))/(a+b))=0

Remove the parentheses from the numerator.
log((a(b))/(a+b))=0

Multiply a by b in the numerator.
log((a*b)/(a+b))=0

Multiply a by b to get ab.
log((ab)/(a+b))=0

Let both sides of the equation be the exponent of base 10.
10^(log((ab)/(a+b)))=10^(0)

When the base of a logarithm in the exponent and the base of the exponent are the same, the result is the argument of the logarithm.
(ab)/(a+b)=10^(0)

Any number raised to the power of 0 is 1.
(ab)/(a+b)=1

Since the variable is in the denominator on the left-hand side of the equation, this can be solved as a ratio. For example, (A)/(B)=C is equivalent to (A)/(C)=B.
(ab)/(1)=(a+b)

Dividing any expression by 1 does not change the value of the expression.
ab=(a+b)

Remove the parentheses around the expression a+b.
ab=a+b

Since a contains the variable to solve for, move it to the left-hand side of the equation by subtracting a from both sides.
ab-a=b

Factor out the GCF of a from each term in the polynomial.
a(b)+a(-1)=b

Factor out the GCF of a from ab-a.
a(b-1)=b

Divide each term in the equation by (b-1).
(a(b-1))/(b-1)=(b)/(b-1)

Simplify the left-hand side of the equation by canceling the common terms.
a=(b)/(b-1)

Answer 21

:D @lalaly

Answer 22

Wow :D