Question

Given log a=b, express 10^2b-3 in terms of a.

Answer 1

Answer:

a^2-3

Step-by-step explanation:

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Answer 2

$\pmb{10^{2b-3}}$  can be expressed as $\pmb{\dfrac{a^2}{1000}}$.

Explanation:

According to the property of logarithm:

 $\log (n) =M\Rightarrow\ \ n=10^M$

Therefore , if $\log a=b\Rightarrow\ \ a=10^b$            (1)

To express $10^{2b-3}$ in term of a.

Consider :  $10^{2b-3} =\dfrac{10^{2b}}{10^3} \ \ [\because\ a^{m-n}=\dfrac{a^m}{a^n}]$

$=\dfrac{(10^b)^2}{1000}\ \[\because\ a^{mn}=(a^m)^n]$

$=\dfrac{a^2}{1000}\ \[\text{From (1)}]$

Hence, $10^{2b-3}$  can be expressed as $\dfrac{a^2}{1000}$.

# Learn more :

If log x = 2a and log y = b/2

then,

1) write 10^ 2b+1 in terms of y

2) if log p = 3a - 2b , express p in terms of x and y