Suppose ${log}_{b} 2 = a$ $Log_b2=a$ and ${log}_{b} 3 = c$ $Log_b3=c$ , how do you find ${log}_{b} (72 b)$ $Log_b(72b)$ ?

Question

Suppose ${log}_{b} 2 = a$ $Log_b2=a$ and ${log}_{b} 3 = c$ $Log_b3=c$ , how do you find ${log}_{b} (72 b)$ $Log_b(72b)$ ?

1 Answer

Impact of this question

6397 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-10T15:24:25

${log}_{b} 72 b = 2 c + 3 a + 1$ $log_b 72b=2c+3a+1$

Explanation:

${log}_{b} 2 = a$ $log_b 2=a$
${log}_{b} 3 = c$ $log_b 3=c$
${log}_{b} 72 b = ?$ $log_b 72b=?$

${log}_{b} 72 b = {log}_{b} 3^{2} \cdot 2^{3} \cdot b$ $log_b 72b=log_b 3^2*2^3*b$

${log}_{x} (k \cdot l \cdot m) = {log}_{x} k + {log}_{x} l + {log}_{x} m$ $log _x ( k*l*m)=log_x k+log_x l+ log _x m$

${log}_{b} 72 b = {log}_{b} 3^{2} + {log}_{b} 2^{3} + {log}_{b} b$ $log_b 72b=log_b 3^2+log _b 2^3+log _b b$

${log}_{b} = 3^{2} = 2 \cdot {log}_{b} 3 = 2 \cdot c$ $log_b=3^2=2*log_b 3=2*c$
${log}_{b} 2^{3} = 3 \cdot {log}_{b} 2 = 3 \cdot a$ $log _b 2^3=3*log _b 2=3*a$
$l o b_{b} b = 1$ $lob_b b=1$

${log}_{b} 72 b = 2 c + 3 a + 1$ $log_b 72b=2c+3a+1$

Science

Math

Humanities

... and beyond

Suppose ${log}_{b} 2 = a$ $Log_b2=a$ and ${log}_{b} 3 = c$ $Log_b3=c$ , how do you find ${log}_{b} (72 b)$ $Log_b(72b)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Suppose logb2=aLog_b2=a and logb3=cLog_b3=c, how do you find logb(72b)Log_b(72b)?

1 Answer

Explanation:

Related questions

Impact of this question

Suppose ${log}_{b} 2 = a$ $Log_b2=a$ and ${log}_{b} 3 = c$ $Log_b3=c$ , how do you find ${log}_{b} (72 b)$ $Log_b(72b)$ ?