Question

Solve for the logarithmic expression: log7 (73 • 78) =

Answer 1

I think your question is ----> $\displaystyle log_7(7^3.7^8)$

we know from exponent rule,
x^m• x^n = x^(m + n)

so, $\displaystyle log_7(7^3.7^8)=log_7(7^{3+8})$

= $\displaystyle log_7(7^{11})$

we know, loga^n = nloga , use it here
= $\displaystyle 11log_77$

we know, $\displaystyle log_aa=1$

= 11

Answer 2

Answer-

The value of the expression is 11

Solution-

The given expression,

$\log_7(7^3.7^8)$

We know that,

$\log_c(a\times b)=\log_c a + \log_c b$

Applying this,

$\log_7(7^3.7^8)=\log_77^3+\log_77^8$

We know that,

$\log_c a^b=b\times \log_c a$

Applying this,

$\log_77^3+\log_77^8=3\times \log_77+8\times \log_77$

We know that,

$\log_aa=1$

Applying this,

$3\times \log_77+8\times \log_77=3\times 1+8\times 1=11$