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Question

two student were given the equation $2^{4x+6} = 3^{6x-3}$

1.steve rearranged to get $2^{4x+6} - 3^{6x-3} =0$

then wrote $\log (2^{4x+6} - 3^{6x-3}) = \log0$

are these legal steps ? if not explain what is wrong with them

2 Ali wrote $\log( 2^{4x+6}) =\log(3^{6x-3})$ then $\log( 2^{4x+6}) - \log(3^{6x-3})=0 $

finally $2^{4x+6} / 3^{6x-3}$

are these legal steps ? if not explain what is wrong with them

Please don't dump questions here without giving a source, a reason to be interested, some evidence that you have actually thought about the problem, and so on. — Gerry Myerson, May 22 '13 at 13:30
@MomenOsama Are you sure? Why do you say that? What's $10^0$? — Calvin Lin, May 22 '13 at 13:32
@MomenOsama, if $10^0=1$ then $\log_{10}1=0$, not $\log_{10}0=1$. — vadim123, May 22 '13 at 13:34
I have a feeling that was supposed to be $2^{4x+6}$, not $2^{4x}+6$, and so on --- but, who knows? — Gerry Myerson, May 22 '13 at 13:34
If you are not going to use $\LaTeX$, please use parentheses to show what you mean. — Ross Millikan, May 22 '13 at 13:39

score 2 · Accepted Answer · answered May 22 '13 at 13:40

2

The first is not legal as you cannot take the log of $0$. The second is legal, but I do not see it as progress toward finding $x$. Ali should use the laws of logarithms to pull down the powers. His finally can be reached in one step from the initial equation and does not give a value for $x$.

answered May 22 '13 at 13:40

Ross Millikan

374,822

thanks Ross Millikan <<< so ali and steve are not correct – Momen Osama May 22 '13 at 13:42

score 1 · Answer 2 · answered May 22 '13 at 13:40

1

Rewrite you equation as $$ \bigg(\frac{2^2}{3^3}\bigg)^{2x}=3^{-3}2^{-6} $$

Can you handle from here?

answered May 22 '13 at 13:40

Alex

19,262

score 0 · Answer 3 · answered May 22 '13 at 18:34

The first task is to get the unknown out of the exponents.

Do not rearrange the equation. Rather, make the substitutions:$$3=e^{\ln (3)}$$ $$2=e^{\ln (2)}$$which yields $$e^{(\ln2)\times (4x+6)} = e^{(\ln 3) \times (6x-3)}$$ Yoe now have two exponential terms, with the same base, equal to each other. The exponents must then be equal. You are left with a simple linear equation with one unknown. (Two of the coefficients are sort of ugly!)

logs Challenge between two students >>be smart

3 Answers3