# Write in exponential form: `log_4 32=x` , `log_10 0.01=-2` and `log_a b=2` . Write in the logarithmic form: `3^4=81` and `(1/2)^4=1/16`

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An equation in the logarithmic form `log_b y = x` can be written in the exponential form as `y = b^x` .

This gives: `log_4 32=x => 32 = 4^x` , `log_10 0.01= -2 => 0.01 = 10^-2` and `log_a b = 2 => b = a^2`

An equation in the exponential form `b^x = a` can be written in the logarithmic form as `x = log_b a`

This gives: `3^4=81 => log_3 81 = 4` and `(1/2)^4=1/16 => log_(1/2) (1/16) = 4`

`1)log_4 32=x` `4^x=32` `2^(2x)=2^5` `2x=5`

`x=5/2`

`2) Log 0.01=-2` `10^(-2)=0.01` `1/(10^2)= 0.01`

`3) log_a b=2` `a^2=b`

`4) 3^4=81` `log_3 81=4`

`5)` `(1/2)^4= 1/16` `log_(1/2) (1/16)=4` `-(-log_2 16)=4`

`log_2 16=4`