Question

What is the solution of log((3x + 4))4096 = 4? ( the 3x+4 is like an exponent but lower

Answer 1

`\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_(3x+4)(4096)=4\implies \stackrel{\textit{exponential form}}{(3x+4)^4=4096}\implies (3x+4)^4=2^(12) \\\\\\ \stackrel{~\hfill \textit{same exponents, the bases must be the same}}{(3x+4)^4=2^(3\cdot 4)\implies (3x+4)^4=(2^3)^4}\implies 3x+4=2^3\implies 3x+4=8 \\\\\\ 3x=4\implies x=\cfrac{4}{3}`