Question

5^a = 6^b = 30^c, then c=?​

Answer 1

Answer:

C=A+B

Step-by-step explanation:

$\tt \: Let \: {5}^{a} = {6}^{b} = {30}^{c} = K \\ --------------------\\ \longrightarrow \tt \: {5}^{a} = K \\ \longrightarrow \: \tt {K}^{ \frac{1}{a} } = 5 \\ -------------------- \\ \longrightarrow \tt \: {6}^{b} = K \\ \longrightarrow \tt \: {K}^{ \frac{1}{b} } = 6 \\ -------------------- \\ \longrightarrow \: \tt {30}^{c} = K \\ \longrightarrow \tt \: {K}^{ \frac{1}{c} } = 30 \\ -------------------- \\ \tt \: We \: know \: that \: 5 \times 6 = 30 \\ \tt So, \\ -------------------- \\ \longrightarrow \tt \: {K}^{ \frac{1}{a} } \times {K}^{ \frac{1}{b} } = {K}^{ \frac{1}{c} } \\ -------------------- \\ \tt So, \: if \: bases \: are \: equal \: \\ \tt \: exponents \: might \: be \: equal \\ -------------------- \\ \longrightarrow \tt \: \frac{1}{a} + \frac{1}{b} = \frac{1}{c} \\ \longrightarrow \tt \: \huge{ \underline { \red{ \boxed{ \tt \blue{ c = a + b}}}}}$