Question

Find the value of log64 withbase 8+log 8 with base 64​

Answer 1

log 64 with base 8=2

since

8²=64

hence,

log 8 with base 64=1/log 64 with base 8

=1/2

so,the answer will be

2+1/2

5/2

Answer 2

$\log_8 {64}+\log_{64} 8=2.5$

Step-by-step explanation:

Given : Expression $\log_8 {64}+\log_{64} 8$

To find : The value of the expression ?

Solution :

Let $\log_8 64=x$

Applying logarithmic property, $\log_b x=y\Rightarrow b^y=x$

i.e. $8^x=64$

$(2^3)^x=(2^6)$

$2^{3x}=2^6$

$3x=6$

$x=\frac{6}{3}$

$x=2$

So, $\log_8 64=2$

Let $\log_{64} 8=y$

Applying logarithmic property, $\log_b x=y\Rightarrow b^y=x$

i.e. $64^y=8$

$(2^6)^y=(2^3)$

$2^{6y}=2^3$

$6y=3$

$y=\frac{3}{6}$

$y=\frac{1}{2}$

$y=0.5$

So, $\log_{64} 8=0.5$

Substitute the value,

$\log_8 {64}+\log_{64} 8=2+0.5$

$\log_8 {64}+\log_{64} 8=2.5$

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