Question

If log₁₀a = b - log₁₀c, find a

Options: 1. $\frac{b}{c}$

2. bc

3. 10ᵇc

4. $\frac{10b}{c}$

Answer 1

$heya \\ \\ \\ log_{10}(a) + log_{10}(c) = b \\ \\ log_{10}(a \times c) = b \\ becoz \: \: \: log(m) + log(n) = log(m \times n) \\ \\ a \times c \: = 10 {}^{b} \\ becoz \: \: \: \: log_{x {}^{} }(y) = z \: \: \: then \: \\ y = x {}^{z} \\ \\ \\ a = 10 {}^{b} \div c$

Answer 2

Hey Buddy

Here's the answer

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# Some useful identities

1. logx ( a ) + logx ( b ) = logx ( a × b )

2. logx ( a ) - logx ( b ) = logx ( a / b ).

3. logx ( a ) = b

=> a = b^( x )

Now solution

=> log₁₀( a ) = b - log₁₀ ( c )

=> log₁₀( a ) + log₁₀ ( c ) = b

using identity ( 1 )

=> log₁₀( a × c ) = b

using identity ( 3 )

=> a × c = 10^b

=> a = [10^ ( b ) ]/c

Hence option ( 4 ) is correct one

HOPE HELPED..

JAI HIND

:)