Question

solve for x, if 8^4x-6= (1/2)^x+5

Answer 1

Have you considered that \(8 = 2^{3}\;and\;1/2 = 2^{-1}\)?

Have you also considered writing correctly, using the Order of Operations and various grouping symbols?

8^4x-6= (1/2)^x+5

You have written \(\left(8^{4}\cdot x\right) - 6\).

I'm guessing you meant \(8^{4x-6}\)

You have written \((1/2)^{x} + 6\).

I'm guessing you meant \((1/2)^{x+5}\)

It is VERY important for you to know the difference.

Answer 2

i know the differnece...

Answer 3

and yes thats what i meant.

Answer 4

\(\bf 8^{4x-6}= \left(\cfrac{1}{2}\right)^{x+5}\quad \textit{taking log to both sides}\\ \quad \\
log\left(8^{4x-6}\right)= log\left[\left(\frac{1}{2}\right)^{x+5}\right]\\ \quad \\
\textit{now recall the log rule of }log(a^x)\implies x\cdot log(a)\)

simplify and solve for "x"

Answer 5

\[8^{4x-6}=\left( \frac{ 1 }{ 2 } \right)^{x+5}\]
\[\left( 2^{3} \right)^{4x-6}=\left( 2^{-1} \right)^{x+5}\]
\[2^{3\left( 4x-6 \right)}=2^{-1\left( x+5 \right)}\]
\[2^{12x-18}=2^{-x-5}\]
12x-18=-x-5
12x+x=-5+18
13x=13
x=1