Question

Given $lo{g}_{10}2=a$ and $lo{g}_{10}3=b$, if $3x+2=25$, the value of x in terms of $a$ and $b$ is $x=({10}^k+1)$. K=?

• A. $\frac{a-1}{b}$
• B. $a-b+1$
• C. $\frac{1+a}{b}$
• D. $\frac{b}{1-a}$

Answer 1

The correct option is B $a-b+1$

${\log }_{10}2=a$

$\Rightarrow 2=\left({10}^a\right)$

${\log }_{10}3=b$

$\Rightarrow 3=\left({10}^b\right)$

$3x+2=25$

$x=\frac{23}{3}=(2\times \frac{10}{3}+1)=10\frac{(10{)}^a}{(10{)}^b}+1$

$x={10}^{(a+1-b)}+1$

$x=({10}^{a-b+1}+1)$