1. ## Logarithms questions

Hi All,

I have the following questions regarding logarithms:

1) If a,b,c are distinct values, what is the value of abc if
(logba)(logca) + (logab) (logcb)+ (logac) (logbc) -3 =0

2) what is the value of x, if y = log7log7x and 5(y/log75) = 2

Assume that logba means Loga to the base b

2. Hello, ayyappakumar!

I hope I read #2 correctly.
You should learn to use parentheses . . .

2) Given: .$\displaystyle {\color{blue}[1]}\;y \:=\: \log_7(\log_7x)\:\text{ and }\:{\color{blue}[2]}\;\frac{5y}{\log_75} \:=\: 2$

find the value of $\displaystyle x.$

From [2], we have: .$\displaystyle y \:=\:\tfrac{2}{5}\log_75\:=\:\log_7\!\left(5^{\fra c{2}{5}}\right)$

Substitute into [1]: .$\displaystyle \log_7(\log_7x) \:=\:\log_7\!\left(5^{\frac{2}{5}}\right)$

Exponentiate: .$\displaystyle \log_7x \:=\:5^{\frac{2}{5}}$

$\displaystyle \text{Exponentiate: }\;x \;=\;7^{\left(5^{\frac{2}{5}}\right)}$

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# Logba.logca logab.logcb logac.logbc=3.abc=1

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