1. ## Log Questions

Express in the simplest form -

log(lower)3(/lower) 23 + 1

1/2 + 3log(lower)10(/lower) x^2

Solve for X

log (lower)x+1(/lower) 27 = 3

-log(lower)3x-1(/lower)1/32 = 5

2. Originally Posted by mibamars

Express in the simplest form -

log(lower)3(/lower) 23 + 1

1/2 + 3log(lower)10(/lower) x^2

Solve for X

log (lower)x+1(/lower) 27 = 3

-log(lower)3x-1(/lower)1/32 = 5

3. Originally Posted by mibamars

...
Solve for X

log (lower)x+1(/lower) 27 = 3

-log(lower)3x-1(/lower)1/32 = 5
Hello,

I assume that you mean:

$\displaystyle \log_{x+1}(27) = 3 \Longleftrightarrow 27 = (x+1)^3 \Longleftrightarrow 3^3 = (x+1)^3 \Longleftrightarrow 3 = x+1 \Longleftrightarrow x = 2$

$\displaystyle -\log_{3x-1}\left( \frac{1}{32}\right) = 5 \Longleftrightarrow \frac{1}{32} = (3x-1)^{-5}$$\displaystyle \Longleftrightarrow 2^{-5}= (3x-1)^{-5} \Longleftrightarrow 2 = 3x-1 \Longleftrightarrow x = 1$

4. Originally Posted by mibamars

Express in the simplest form -

log(lower)3(/lower) 23 + 1

1/2 + 3log(lower)10(/lower) x^2

...
Hello,

not certain if you are looking for this:

$\displaystyle \log_{3}(23) + 1 \Longrightarrow \log_{3}(23) + \log_{3}(3) = \log_{3}(23 \cdot 3) = \log_{3}(69)$

$\displaystyle \frac{1}{2}+3 \cdot \log_{10}(x^2) = \log_{10}(\sqrt{10}) + \log_{10}(x^6) = \log_{10}( \sqrt{10} \cdot x^6)$