$8^a=3$ and $3^b=5$ and $10^c=5$ then find $c$ in terms of $a$ and $b$. if $8^a=3$ and $3^b=5$ and $10^c=5$ then find $c$ using $a$ and $b$.
My Attempt:
if $8^a=3$ and $3^b=5$ then we can say that $8^{ab}=5$ and then we have $2^{3ab}=10^c$ but i cant solve this equation.

$$8^a=3\implies3a\log2=\log3$$
Similarly, $$b\log3=\log5$$ and $$\log5=c(\log5+\log2)\iff(c-1)\log5=c\log2$$
$$\implies3a\log2\cdot b\log3\cdot(c-1)\log5=\log3\cdot \log5\cdot c\log2$$
$$\iff3a\cdot b(c-1)=c$$
See: Laws of Logarithms
