Question

log 2 base 10 =x and log 3 base 10 = y what is log 60 base 10
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Answer 1

log²10=x

log³10=y

log ⁶⁰10=log⁶10+log¹⁰10

=log²10+log³10+log¹⁰10

=x+y+1

:.value of log⁶⁰10=x+y+1

pls mark brainliest

Answer 2

$\bigstar$ Explanation $\bigstar$

$\longrightarrow$ Given:-

$\log_{10} 2 = x ----\: \sf eqn (i)$

$\log_{10} 3 = y----\: \sf eqn (ii)$

$\longrightarrow$ To find:-

Value of $\log_{10} 60$

$\longrightarrow$ Solution:-

We know that,

$\log_{x} abc = \log_xa + \log_xb + \log_xc$

Therefore,

$log_{10} 60 = \log_{10}(2 \times 3 \times 10)$

$\log_{10} 60 = \log_{10} 2 + \log_{10}3 + \log_{10} 10$

From eqn (i) and eqn (ii),

$log_{10} 60 = x + y + 1$  [ We know that $log_{a} a = 1$ ]

$\longrightarrow$ Formulas related to logarithms:-

i) $\log_x y = z \implies x^z = y$

ii) $\ln(x) = \log_e x$

iii) $\log_x(ab) = \log_xa + \log_xb$

iv) $\log_x\frac{a}{b} = \log_xa-\log_xb$

v) $\log_aa = 1$

vi) $\log_{b} a = \dfrac{\log_x a}{\log_x b} = \dfrac{1}{\log_a b}$